text:
\section{Introduction}

In scalar-on-function regression, parametric regression models are useful for interpreting the linear relationship between scalar response and functional predictor, while nonparametric regression models may capture a possible nonlinear relationship, and thus may improve the estimation and prediction accuracies of the regression function. By combining the advantages of parametric and nonparametric regression models, the semiparametric regression models, such as the functional partial linear model, have received increasing attention in the literature \citep[e.g.,][]{Lian11}.

Despite rapid developments in the estimations of functional partial linear models, the optimal selections of semi-metric and bandwidth remain largely unexplored. To address this, we consider the optimal parameter selections from the perspective of error-density estimation in functional regression. The estimation of error density is important for understanding the residual behavior of regression models and assessing the adequacy of the error distribution assumption \citep[e.g.,][]{AV01, CS08}. The estimation of error density is also useful for testing the symmetry of the residual distribution \citep[e.g.,][]{AL97, ND07}; for the estimation of the density of response variable \citep[e.g.,][]{EJ12}; and is important for statistical inference, prediction and model validation \citep[e.g.,][]{Efromovich05, MN10}.

In a nonparametric scalar-on-function regression, \cite{Shang13} proposes a Bayesian bandwidth estimation method for determining the bandwidth of the Nadaraya-Watson (NW) estimator for estimating regression mean function and the bandwidth of the kernel-form error density. Also, in nonparametric scalar-on-function regression, \cite{Shang16} proposes a Bayesian bandwidth estimation method for determining the bandwidth of the NW estimator for estimating regression quantile function and the bandwidth of the kernel-form error density. Further, \cite{Shang16} uses marginal likelihood as a means of selecting the optimal semi-metric. Building on the early work by \cite{ZKS11}, \cite{ZK11} and \cite{Shang13, Shang14, Shang13b, Shang16, Shang19}, we consider a kernel error-density estimator which explores data-driven features, such as asymmetry, skewness, and multi-modality, and relies on residuals obtained from the estimated regression function and bandwidth of residuals. Differing from those early work, we derive an approximate likelihood and a posterior for the functional partial linear model (a semiparametric model). We present a Markov chain Monte Carlo (MCMC) sampling algorithm for simultaneously sampling bandwidth parameters, linear regression coefficient function $\beta(t)$, and nonlinear NW estimator of $m(z)$. Through a series of simulation studies, the functional partial linear model gives improved estimation and forecast accuracies of the regression mean function compared with the functional principal component regression and nonparametric scalar-on-function regression.

While the selection of bandwidth determines the amount of smoothing, the selection of semi-metric plays an important role in measuring distances among functions. In nonparametric functional data analysis, the optimal bandwidth can be determined either by functional cross-validation \citep{RV07} or by a Bayesian method incorporating the information on error density \citep{Shang13}. However, the optimal selection of semi-metric is rather arbitrary. As noted by \citet[][Chapters 3 and 13]{FV06}, a semi-metric based on a derivative should be used for a set of smooth functional data; a semi-metric based on a dimension-reduction technique, such as functional principal component analysis (FPCA), should be used for a set of rough functional data. To the best of our knowledge, little attention has been paid for selecting which semi-metric is adequate based on rigorous statistical criteria.

This lack of rigorous statistical criteria motivates our investigation of a Bayesian method for estimating bandwidths in the regression function and error density simultaneously, and for selecting the optimal semi-metric, based on the notion of marginal likelihood (also referred to \cite{KR95} as the evidence). The marginal likelihood reflects a summary of evidence provided by the data supporting a choice of semi-metric as opposed to its competing semi-metric. The optimal semi-metric is that which has the largest marginal likelihood. With the marginal likelihood, it is straightforward to calculate the Bayes factor for measuring the strength of evidence between any two semi-metrics \citep[e.g.,][]{KR95}. Selecting the optimal semi-metric and bandwidths often improves the estimation and prediction accuracies of the regression function, including the functional partial linear model considered here.

The remainder of this paper is organized as follows. In Section~\ref{sec:2}, we introduce the partial linear model with the functional covariate, previously studied by \cite{Lian11}, and the estimation procedure in \cite{AV15}, \cite{AFV15} and \cite{NAV17}. In Section~\ref{sec:3}, we review the Bayesian bandwidth-estimation method and introduce the notion of marginal likelihood computed as a by-product of the MCMC. The optimal semi-metric is determined by having the largest marginal likelihood among several possible semi-metrics. Using a series of simulation studies in Section~\ref{sec:4}, we evaluate and compare the estimation accuracies of the regression function and error density. Also, we compare the forecast accuracy of regression function among the functional partial linear model, functional principal component regression, and functional nonparametric regression. In Section~\ref{sec:5}, we apply the proposed method to a spectroscopy dataset in the food quality control and compare its forecast accuracy with 13 commonly used functional regression models. Conclusions are presented in Section~\ref{sec:6}, along with some reflections on how the method presented here could be extended.

\section{Model and estimator}\label{sec:2}

There is an increasing amount of literature on the development of nonparametric functional estimators, such as the functional NW estimator \citep{FV06}, the functional local-linear estimator \citep{BEM11}, the functional $k$-nearest neighbor estimator \citep{BFV09}, and the distance-based local-linear estimator \citep{BDF10}. In the functional partial linear model, we choose to estimate the \textit{conditional mean} by the functional NW estimator because of its simplicity and robustness against a large gap in design points.

\subsection{A functional partial linear model}

When modeling scalar responses and functional predictors, some functional variables are related to responses linearly while other variables have nonlinear relationships with the response. We consider a random data triplet $(\mathcal{X}, \mathcal{Z}, y)$, where $y$ is a real-valued response and the functional random variable $\mathcal{X}$ is valued in Hilbert space containing square-integrable functions and $\mathcal{Z}$ is valued in some infinite-dimensional semi-metric vector space $(\mathcal{F}, d(\cdot,\cdot))$. Let $(\mathcal{X}_i, \mathcal{Z}_i, y_i)_{i=1,2,\dots,n}$ be a sample of data triplets that are independent and identically distributed (iid) as $(\mathcal{X}, \mathcal{Z}, y)$. We consider a functional partial linear model with homoscedastic errors. Given a set of observations $(\mathcal{X}_i, \mathcal{Z}_i, y_i)$, the regression model can be expressed as
\begin{equation*}
y_i = \int_{t\in\mathcal{I}} \mathcal{X}_i(t)\beta(t)dt + m(\mathcal{Z}_i) + \varepsilon_i,
\end{equation*}
where $\mathcal{I}$ represents function support range, $\beta(\cdot)$ is a regression coefficient function, $m(\cdot)$ is an unknown smooth real function that captures the possible nonlinear relationship between $\mathcal{Z}$ and $y$ and $(\varepsilon_1,\dots,\varepsilon_n)$ are iid random error satisfying
\begin{equation*}
\text{E}\left(\varepsilon_i|\mathcal{X}_i, \mathcal{Z}_i\right) = 0.
\end{equation*}

Following the estimation procedure of \cite{AV06}, it is natural to estimate the regression coefficient function $\beta(\cdot)$ and the smooth function $m(\cdot)$ by the ordinary least squares and functional NW estimators, given by
\begin{align}
\widehat{\beta}_h(t) &= \left[\bm{\widetilde{\mathcal{X}}}^{\top}_h(t)\bm{\widetilde{\mathcal{X}}}_h(t)\right]^{+}\bm{\widetilde{\mathcal{X}}}_h^{\top}(t)\bm{\widetilde{y}}_h,\label{eq:3} \\
\widehat{m}_h(z) &= \sum_{i=1}^nw_h(z,\mathcal{Z}_i)\left[y_i-\langle\mathcal{X}_i(t), \widehat{\beta}_h(t)\rangle\right],\label{eq:4}
\end{align}
where $^{+}$ represents generalized inverse and $^{\top}$ represents the column vector; $\bm{\mathcal{X}} = \left(\mathcal{X}_1,\dots,\mathcal{X}_n\right)^{\top}$ and $\bm{y}=\left(y_1,\dots,y_n\right)^{\top}$, $\bm{\widetilde{\mathcal{X}}}_h=(\bm{I}-\bm{W}_{h})\bm{\mathcal{X}}$ and $\widetilde{\bm{y}}_h = (\bm{I}-\bm{W}_h)\bm{y}$, $\bm{W}_h = \left[w_{h}(\mathcal{Z}_i, \mathcal{Z}_j)\right]_{i,j}$ is a weight matrix with $w_h\big(z,\mathcal{Z}_i\big)$ being the NW-type weights,
\begin{equation*}
w_h(z,\mathcal{Z}_i) = \frac{K\left[d(z,\mathcal{Z}_i)/h\right]}{\sum^n_{j=1}K\left[d(z,\mathcal{Z}_j)/h\right]},
\end{equation*}
where $K(\cdot)$ is a kernel function, such as the Gaussian kernel function considered in this paper, $h$ is a positive real-valued estimated bandwidth parameter, controlling the trade-off between squared bias and variance in the mean squared error (MSE) and $d(\cdot,\cdot)$ is a semi-metric used to quantify differences among curves.

The regression coefficient function $\widehat{\beta}_h(t)$ in~\eqref{eq:3} can be seen as the ordinary least squares estimator obtained by regressing the partial residual vector $\widetilde{\bm{y}}_h$ on the partial residual vector of functions $\widetilde{\bm{\mathcal{X}}}_h$. To avoid possible non-singularity, it is common to use a dimension-reduction technique, such as functional principal component regression  \citep[e.g.,][]{RO07, RGS+17, Lian11}. However, $\widehat{m}_h(z)$ in~\eqref{eq:4} can be seen as the functional NW estimator, with the partial residual vector as the response variable. Therefore, the estimation accuracy of $\widehat{\beta}_h(t)$ and $\widehat{m}_h(z)$ crucially depends on the optimal estimation of $h$. With an estimated bandwidth of the NW estimator, we obtain an estimate of $\beta(t)$ at each iteration of the MCMC sampling. Then, we take average over all iterations to obtain the final estimates, namely $\widehat{h}$, $\widehat{\beta}_h(t)$ and $\widehat{m}_h(z)$.

In functional nonparametric regression, the bandwidth parameter is commonly determined by functional cross-validation \citep[e.g.,][]{FV09, BFV09, BFV10, FHV10}. Functional cross-validation aims to select a bandwidth that minimizes the squared loss function and has the appealing feature that no estimation of the error variance is required. However, as stated, an accurate estimation of error density is important. Thus, we consider a Bayesian method to estimate bandwidth parameters in the regression function and error density simultaneously. The Bayesian method aims to select a bandwidth that minimizes the Kullback-Leibler (KL) divergence.

\subsection{Choice of semi-metric}

The choice of semi-metric has effects on the size and form of neighborhoods and can thus control the concentration properties of functional data. Although \citet[][p.193]{FV06} note that the selection of the semi-metric remains an open question, there is no method to quantify which semi-metric is adequate, or how to select the optimal semi-metric, using statistical criteria.

From a practical perspective, the semi-metric based on derivative should be utilized for a set of smooth functional data. This semi-metric can be expressed as
\begin{equation*}
d_q^{\text{deriv}}(\mathcal{Z}_i,\mathcal{Z}) = \sqrt{\int_t\left[\mathcal{Z}_i^{(q)}(t) - \mathcal{Z}^{(q)}(t)\right]^2dt},
\end{equation*}
where $\mathcal{Z}^{(q)}$ is the $q$\textsuperscript{th}-order derivative of $\mathcal{Z}$, in which first and second derivatives are commonly used in practice \citep[e.g.,][]{Goutis98, FV02, FV09}. Computationally, the semi-metric based on the $q$\textsuperscript{th}-order derivative uses a $B$-spline approximation for each curve, and a derivative of a $B$-spline function can be directly computed by differencing the $B$-spline coefficients and $B$-spline basis functions of one order lower \citep[for more detail, see][Section 3.4]{deBoor01, FV06}.

For a set of rough functional data, a semi-metric based on FPCA is commonly used \citep[for detail on the choice of semi-metric from the practical and theoretical perspectives, see][Chapters 3 and 13]{FV06}. The semi-metric based on FPCA computes proximities among a set of rough curves using the principal component scores. FPCA reduces the functional data to a finite-dimensional space (i.e., $K$ number of components). The finite-dimensional representation can be expressed as
\begin{equation*}
d_K(\mathcal{Z}_i,\mathcal{Z}) \approx \sqrt{\sum^K_{\zeta=1}(\beta_{\zeta,i}-\beta_{\zeta})^2\|\phi_{\zeta}(t)\|^2},
\end{equation*}
where $K$ represents the number of retained functional principal components, and $\|v\|=\sqrt{\langle v,v\rangle}$ represents the induced norm.

\section{Bayesian method}\label{sec:3}

In Section~\ref{sec:3.1}, we briefly review \citeauthor{Shang13}'s \citeyearpar{Shang13} Bayesian method for selecting optimal bandwidth. As a by-product of the MCMC, the optimal semi-metric can be determined with the largest marginal likelihood among a set of semi-metrics (as presented in Section~\ref{sec:3.2}).

\subsection{Bayesian bandwidth estimation}\label{sec:3.1}

\cite{ZKS11} consider a kernel-form error density in a nonparametric regression model, while \cite{ZK11} consider the kernel-form error density in a nonlinear parametric model where Bayesian sampling approaches are used. Following the early work by \cite{ZKS11} and \cite{ZK11}, the unknown error density $f(\varepsilon)$ can be approximated by a location-mixture Gaussian density, given by
\begin{equation*}
f(\varepsilon;b) = \frac{1}{n}\sum^n_{j=1}\frac{1}{b}\phi\left(\frac{\varepsilon-\varepsilon_j}{b}\right),
\end{equation*}
where $\phi(\cdot)$ is the probability density function of  the standard Gaussian distribution and Gaussian densities have means at $\varepsilon_j$, for $j=1,2,\dots,n$ and a common standard deviation $b$.

Given that errors are unknown in practice, we approximate them by residuals obtained from the functional principal component and functional NW estimators of the conditional mean. Given bandwidths $h$ and $b$, the kernel likelihood of $\bm{y} = (y_1,\dots,y_n)^{\top}$ is given by
\begin{equation}
\widehat{L}\left(\bm{y}|h,b\right) = \prod^n_{i=1}\Bigg[\frac{1}{n-1}\sum^n_{\substack{j=1\\ j\neq i}}\frac{1}{b}\phi\left(\frac{\widehat{\varepsilon}_{i}-\widehat{\varepsilon}_{j}}{b}\right)\Bigg],\label{eq:5}
\end{equation}
where $\widehat{\varepsilon}_i=y_i - \int_{t\in \mathcal{I}}\mathcal{X}_i(t)\widehat{\beta}(t)dt - \widehat{m}(\mathcal{Z}_i)$ represents $i$\textsuperscript{th} residual obtained from the estimated regression function. This likelihood is not proper since some terms are left out. Instead, the likelihood is a pseudo-likelihood. The pseudo-likelihood is a likelihood function associated with a family of probability distributions, which does not necessarily contain the true function \citep{GMT84}. As a consequence, the resulting Bayesian estimators, while consistent, may have an inaccurate posterior variance, and subsequent credible sets constructed by this posterior may not be asymptotically valid \citep[see also][]{VH03, Mueller13}.

By assuming that the independent priors of squared bandwidths $h^2$ and $b^2$ follow inverse Gamma distribution $\text{IG}\left(10^{-3},10^{-3}\right)$, the posterior density can be obtained by multiplying the kernel likelihood in~\eqref{eq:5} with the prior density. The posterior density can be expressed as (up to a normalizing constant)
\begin{equation*}
\pi\left(h^2,b^2|\bm{y}\right) \propto \widehat{L}\left(\bm{y}|h,b\right) \times \pi\left(h^2\right)\times \pi\left(b^2\right).\label{eq:posterior}
\end{equation*}

\subsection{Sampling algorithm}\label{sec:3.3}

Computationally, an adaptive random-walk Metropolis algorithm can be used for sampling both parameters $(h,b)$ iteratively \citep[see][]{GFS10}. The sampling procedure is briefly described as follows:
\begin{enumerate}
\item[1)] Specify a Gaussian proposal distribution and begin the sampling iteration process by choosing an arbitrary value of $(h^2, b^2)$ and denoting it as $(h_{(0)}^2, b_{(0)}^2)$. The starting points can be drawn from a uniform distribution $U(0,1)$.
\item[2)] From the initial bandwidths $h_{(0)}^2$ and $b_{(0)}^2$, we obtain an initial estimate of linear regression coefficient function, $\widehat{\beta}_{h_{(0)}}(t)$ from~\eqref{eq:3} and an initial estimate of nonlinear regression function, $\widehat{m}_{h_{(0)}}(z)$ from~\eqref{eq:4}.
\item[3)] At the $k$\textsuperscript{th} iteration, the current state $h_{(k)}^2$ is updated as $h_{(k)}^2=h_{(k-1)}^2+\tau_{(k-1)}u$, where $u$ is drawn from the proposal density which can be the standard Gaussian density and $\tau_{(k-1)}$ is an adaptive tuning parameter with an arbitrary initial value $\tau_{(0)}$. The updated $h_{(k)}^2$ is accepted with a probability given by
\begin{equation*}
\min\left\{\frac{\pi\left(h^2_{(k)},b^2_{(k-1)}\big|\bm{y}\right)}{\pi\left(h^2_{(k-1)},b^2_{(k-1)}\big|\bm{y}\right)},1\right\}.
\end{equation*}
\item[4)] The tuning parameter for the next iteration is set to
\[ \tau_{(k)} = \left\{ \begin{array}{ll}
\tau_{(k-1)}+c(1-\xi)/k & \mbox{\qquad if $h^2_{(k)}$ is accepted} \\
\tau_{(k-1)}-c\xi/k & \mbox{\qquad if $h^2_{(k)}$ is rejected} \end{array} \right.\]
where $c=\tau_{(k-1)}/(\xi-\xi^2)$ is a constant and $\xi$ is the optimal target acceptance probability, which is 0.44 for univariate updating \citep[e.g.,][]{RR09}.
\item[5)] Conditional on $h_{(k)}^2$ and $\bm{y}$, we obtain an estimator of linear regression coefficient function, $\widehat{\beta}_{h_{(k)}}(t)$, and an NW estimator of nonlinear regression function, $\widehat{m}_{h_{(k)}}(z)$ \citep[see, e.g.,][]{CSZ17}.
\item[6)] Repeat Steps 2-5 for $b_{(k)}^2$, conditional on $h_{(k)}^2$ and $\bm{y}$.
\item[7)] Repeat Steps 2-6 for $M+N$ times, discard $\big(h^2_{(0)}, \beta_{h_{(0)}}(t), m_{h_{(0)}}(z), b^2_{(0)}\big)$, $\big(h^2_{(1)}, \beta_{h_{(1)}}(t), m_{h_{(1)}}(z), b^2_{(1)}\big)$, \\ $\dots$, $\left(h^2_{(M)}, \beta_{h_{(M)}}(t), m_{h_{(M)}}(z), b^2_{(M)}\right)$ for burn-in to let the effects of the transients wear off, estimate $\widehat{h}^2 = \frac{\sum^{M+N}_{k=M+1}h_{(k)}^2}{N}$, $\widehat{\beta}_{h}(t) = \frac{\sum^{M+N}_{k=M+1}\beta_{h_{(k)}}(t)}{N}$, $\widehat{m}_{h}(z) = \frac{\sum^{M+N}_{k=M+1}m_{h_{(k)}}(z)}{N}$, and $\widehat{b}^2=\frac{\sum^{M+N}_{k=M+1}b_{(k)}^2}{N}$. The burn-in period is taken to be $M=1,000$ iterations and the number of iterations after the burn-in is $N=10,000$ iterations.
\end{enumerate}

\subsection{Bayesian model selection}\label{sec:3.2}

In Bayesian inference, model selection is often conducted through the marginal likelihood of the model of interest against a competing model. The marginal likelihood is the expectation of likelihood with respect to the prior density of parameters and reflects a summary of evidence provided by the data supporting the model as opposed to its competing model. It is seldom calculated as the integral of the product of the likelihood and prior density of parameters, but instead, is often computed numerically \citep[e.g.,][]{GD94, Chib95}. We use the method proposed by \cite{Chib95} to compute the marginal likelihood.

Let $\bm{\theta}=\left(h,b\right)$ be the parameter vector and $\bm{y}=\left(y_1,\dots,y_n\right)$ be the data. \cite{Chib95} demonstrated that the marginal likelihood under model $A$ can be expressed as
\begin{equation*}
L_{\text{A}}(\bm{y}) = \frac{L_{\text{A}}(\bm{y}|\bm{\theta})\pi_{\text{A}}(\bm{\theta})}{\pi_{\text{A}}(\bm{\theta}|\bm{y})},
\end{equation*}
where $L_{\text{A}}(\bm{y}|\bm{\theta})$, $\pi_{\text{A}}(\bm{\theta})$ and $\pi_{\text{A}}(\bm{\theta}|\bm{y})$ denote the likelihood, prior and posterior, respectively. $L_{\text{A}}(\bm{y})$ is often computed at the posterior estimate of $\bm{\theta}$. The numerator has a closed form and can be computed analytically. The denominator can be estimated by its kernel-density estimator based on the simulated samples of $\bm{\theta}$ through a posterior sampler. Based on marginal likelihoods, the Bayes factor of model A against model B is defined as $L_{\text{A}}(\bm{y})/L_{\text{B}}(\bm{y})$, which can be used to decide whether model A or B is preferred, along with its degree of preference \citep{KR95}.

\subsection{Adaptive estimation of error density}

In the kernel-density estimation of directly observed data, it has been noted that the leave-one-out estimator is profoundly affected by extreme observations in the sample \citep[e.g.,][]{Bowman84}. When the actual error density has sufficient long tails, the leave-one-out kernel-density estimator with a global bandwidth estimated under the KL divergence is likely to overestimate the tails of the density \citep{Shang13}. To address this issue, \cite{ZK11} and \cite{Shang16} suggested that localized bandwidths should improve the estimation accuracy of error density for the symmetrical unimodal distribution. The kernel density estimator with localized bandwidths assigns small bandwidths to the observations in the high-density region and large bandwidths to the observations in the low-density region. The localized error-density estimator can be written as
\begin{equation*}
\widehat{f}\left(\varepsilon_i;\tau,\tau_{\varepsilon}\right) = \frac{1}{n-1}\sum^n_{\substack{j=1\\ j\neq i}}\frac{1}{\tau\left(1+\tau_{\varepsilon}|\widehat{\varepsilon}_j|\right)}\phi\left(\frac{\widehat{\varepsilon}_i-\widehat{\varepsilon}_j}{\tau\left(1+\tau_{\varepsilon}|\widehat{\varepsilon}_j|\right)}\right),
\end{equation*}
where $\tau(1+\tau_{\varepsilon}|\widehat{\varepsilon}_j|)$ is the bandwidth assigned to $\widehat{\varepsilon}_j$, for $j=1,2,\dots,n$ and the vector of parameters is now $(h, \tau, \tau_{\varepsilon})$. The adaptive random-walk Metropolis algorithm, described in Section~\ref{sec:3.3}, can be used for sampling parameters, where the prior density of $\tau_{\varepsilon}\sim U(0,1)$.

\section{Simulation}\label{sec:4}

The principal aim of this section is to illustrate the proposed method through simulated data. We consider two cases in which simulated curves are smooth in Section~\ref{sec:smooth} and in which simulated curves are rough in Section~\ref{sec:rough}. Using the error criteria in Sections~\ref{sec:4.1} and~\ref{sec:4.2}, we assess the estimation accuracies of the regression function and error density, respectively. In Section~\ref{sec:4.4}, we conduct a prior sensitivity analysis.

\subsection{Criteria for assessing estimation and prediction accuracies of the regression function}\label{sec:4.1}

To measure the estimation accuracy of the regression function, we first calculate the averaged mean squared error (AMSE) between the true regression function $g(\cdot)$ and the estimated regression function $\widehat{g}(\cdot)$. This is expressed as
\begin{align*}
\text{AMSE} = \text{E}\left\{\left[g(\mathcal{X}; \mathcal{Z}) - \widehat{g}(\mathcal{X}; \mathcal{Z})\right]^2\right\}&=\text{E}\left(\text{E}\left\{\left[g\left(\mathcal{X}; \mathcal{Z}\right)-\widehat{g}\left(\mathcal{X}; \mathcal{Z}\right)\right]^2\big|\mathcal{X}, \mathcal{Z}\right\}\right) \\
&\approx \frac{1}{n}\sum^n_{i=1}\text{E}\left\{\left[g(\mathcal{X}; \mathcal{Z})-\widehat{g}(\mathcal{X}; \mathcal{Z})\right]^2\big|\mathcal{X}=\mathcal{X}_i, \mathcal{Z} = \mathcal{Z}_i\right\}\\
&\approx\frac{1}{n}\frac{1}{B}\sum^n_{i=1}\sum^B_{s=1}\left[g(\mathcal{X}_i; \mathcal{Z}_i) - \widehat{g}^s(\mathcal{X}_i; \mathcal{Z}_i)\right]^2,
\end{align*}
where $B=100$ represents the number of replications.

To measure the prediction accuracy of the regression function, we calculate the averaged mean squared prediction error (AMSPE) between the holdout regression function $g(\mathcal{X}_{\text{new}}; \mathcal{Z}_{\text{new}})$ and the predicted regression function $\widehat{g}(\mathcal{X}_{\text{new}}; \mathcal{Z}_{\text{new}})$. This is expressed as
\begin{align*}
\text{AMSPE} &= \text{E}\left\{\left[g(\mathcal{X}_{\text{new}}; \mathcal{Z}_{\text{new}}) - \widehat{g}(\mathcal{X}_{\text{new}}; \mathcal{Z}_{\text{new}})\right]^2\right\}\\
&\approx \frac{1}{\eta}\frac{1}{B}\sum^{\eta}_{j=1}\sum^B_{s=1}\left[g(\mathcal{X}_j; \mathcal{Z}_j) - \widehat{g}^s(\mathcal{X}_j; \mathcal{Z}_j)\right]^2,
\end{align*}
where $\eta$ represents the length of prediction samples.

\subsection{Criteria for assessing error-density estimation}\label{sec:4.2}

To measure the difference between the true error density $f(\varepsilon)$ and the estimated error density $\widehat{f}(\varepsilon)$, we consider two risk functions.  First, we calculate the mean integrated squared error (MISE), which is given by
\begin{eqnarray*}
\text{MISE}\left[\widehat{f}(\varepsilon)\right] = \int^b_{\varepsilon=a} \left[f(\varepsilon)-\widehat{f}(\varepsilon)\right]^2d\varepsilon,
\end{eqnarray*}
for $\varepsilon\in [a,b]$. For each replication, the MISE can be approximated at 1,001 grid points bounded between a closed interval, such as $[-10,10]$. These can be expressed as
\begin{eqnarray*}
\text{MISE}\left[\widehat{f}(\varepsilon)\right]\approx \frac{1}{50}\sum^{1001}_{i=1}\left\{f\Big[-10+\frac{(i-1)}{50}\Big]-\widehat{f}\Big[-10+\frac{(i-1)}{50}\Big] \right\}^2.
\end{eqnarray*}
From an average of 100 replications, the approximated mean integrated squared error (AMISE) is used to assess the estimation accuracy of error density. The AMISE is defined as
\begin{eqnarray*}
\text{AMISE}=\frac{1}{B}\sum^B_{b=1}\text{MISE}_b.
\end{eqnarray*}

The second risk function is the KL divergence, given by
\begin{eqnarray*}
\text{KL}\left(\widehat{f}, f\right) = -\text{E}\int_{\varepsilon=a}^b f(\varepsilon)\ln \widehat{f}(\varepsilon)d\varepsilon.
\end{eqnarray*}
With $f$ fixed in simulation, $\text{KL}\left(\widehat{f}, f\right)$ is minimized for $f=\widehat{f}$ \citep{Kullback59}.

\subsection{Simulation of smooth curves}\label{sec:smooth}

We describe the construction of the simulated data. First, we build simulated discretized curves as
\begin{equation}
\mathcal{X}_i(t_j) = a_i\cos(2t_j) + b_i\sin(4t_j) + c_i\Big(t_j^2-\pi t_j + \frac{2}{9}\pi^2\Big), \qquad i=1,2,\dots,n,\label{eq:simu}
\end{equation}
where $t$ represents the function support range and $0\leq t_1\leq t_2\leq \dots \leq t_{100}\leq \pi$ are equispaced points within the function support range, $a_i$, $b_i$, $c_i$ are independently drawn from a uniform distribution on $[0,1]$, and $n$ represents the sample size. The functional form of~\eqref{eq:simu} is taken from \cite{FVV10} and \cite{Shang13, Shang13b}. Figure~\ref{fig:1} presents a replication of 100 simulated smooth curves, along with the first-order derivative of the curves approximated by B-splines.
\begin{figure}[!ht]
\centering
\subfloat[Raw functional curves]
{\includegraphics[width=8.5cm]{Fig_1a}\label{fig:1a}}
\qquad
\subfloat[First-order derivative of the curves]
{\includegraphics[width=8.5cm]{Fig_1b}\label{fig:1b}}
\caption{100 simulated smooth curves.}\label{fig:1}
\end{figure}

\newpage
Once the curves are formed, we define $\mathcal{Z}$ as the first-order derivative of the curves \citep[see also][]{MP09}. We compute the response variable through the following steps:
\begin{enumerate}
\item[1)] Construct a regression-function operator $g$, which performs the mapping from function-valued space to real-valued space. The regression-function operator $g$ is expressed as
\begin{equation*}
g(\mathcal{X}_i; \mathcal{Z}_i) = 10\times \left(a_i^2-b_i^2\right).
\end{equation*}
\item[2)] Generate $\varepsilon_1,\varepsilon_2,\dots,\varepsilon_n$, which are independently drawn from mixture normal distributions. To highlight the possible non-normality of the error density, we consider three different error densities previously introduced by \cite{MW92}:
\begin{enumerate}
\item unimodal symmetric distribution, such as $t_5$;
\item skewunimodal distribution: $0.2\times \text{N}(0,1) + 0.2\times \text{N}\left(0.5,(\frac{2}{3})^2\right) + 0.6\times \text{N}\left(13/12,(\frac{5}{9})^2\right)$;
\item skewbimodal distribution: $0.75\times \text{N}(0,1) + 0.25\times \text{N}\left(1.5,(\frac{1}{3})^2\right)$.
\end{enumerate}
\item[3)] Compute the corresponding responses: $y_i = g(\mathcal{X}_i; \mathcal{Z}_i) + \varepsilon_i$, for $i=1,2,\dots,n$.
\end{enumerate}

\subsubsection{Estimating the regression function}

For a given data triplet ($\mathcal{X}, \mathcal{Z}, y$) and a bandwidth $h$, we compute the discrepancy between $g(\cdot)$ and $\widehat{g}(\cdot)$. We use the following Monte-Carlo scheme:
\begin{itemize}
\item Build 100 replications $\left[(\mathcal{X}_i^{s}, \mathcal{Z}_i^{s}, y_i^{s})_{i=1,\dots,n}\right]_{s=1,\dots,100}$;
\item Compute 100 estimates $\left[g(\cdot)-\widehat{g}^s(\cdot)\right]_{s=1,\dots,100}$, where $\widehat{g}^s(\cdot)$ is the functional NW estimator of the regression function computed over the $s$\textsuperscript{th} replication;
\item Obtain the AMSE and AMSPE by averaging over 100 replications of MSE and MSPE.
\end{itemize}

Table~\ref{tab:1} presents the AMSEs and AMSPEs for the estimated conditional mean, where the error density is estimated by a kernel error density with a global bandwidth and localized bandwidths. The functional partial linear model considers two function-valued random variables, $\mathcal{X}$ and $\mathcal{Z}$. In contrast, functional principal component regression and functional nonparametric regression models consider only the original functional curves, $\mathcal{X}$. Thus, the functional partial linear model produces improved estimation and forecast accuracies than functional principal component regression and functional nonparametric regression.  It is also advantageous to estimate error density with localized bandwidths to achieve the best estimation and forecast accuracies of the regression function. An exception is in the skewbimodal error density, where the difference between the two bandwidth procedures is quite small. Among the three types of semi-metrics, the AMSEs are smaller for the two semi-metrics based on derivatives, compared with the semi-metric based on FPCA. Following the early work by \cite{Shang13b}, we use three retained principal components that seem to be sufficient to capture the primary mode of variation in this example. The semi-metric based on the second derivative has the smallest AMSE and AMSPE among the three semi-metrics.

\begin{center}
\tabcolsep 0.05in
\begin{longtable}{@{}ll|lll|lll|lll@{}}
\caption{Comparisons of the estimation and forecast accuracies of the regression function for the functional partial linear model, functional principal component regression, and functional nonparametric regression for the three choices of semi-metric. The underscore G and L represent a global bandwidth or localized bandwidths for estimating error density. The smallest errors are highlighted in bold.}\label{tab:1} \\
\toprule
& & \multicolumn{9}{c}{Type of semi-metric} \\
& & \multicolumn{3}{c}{$1^{\text{st}}$ derivative} & \multicolumn{3}{c}{$2^{\text{nd}}$ derivative} &\multicolumn{3}{c}{FPCA$_{Z=3}$} \\
& FPCR & FPLM$_{\text{G}}$ & FPLM$_{\text{L}}$ & FNP & FPLM$_{\text{G}}$ & FPLM$_{\text{L}}$ & FNP & FPLM$_{\text{G}}$ & FPLM$_{\text{L}}$ & FNP \\\toprule
\endfirsthead
\toprule
& & \multicolumn{9}{c}{Type of semi-metric} \\
& & \multicolumn{3}{c}{$1^{\text{st}}$ derivative} & \multicolumn{3}{c}{$2^{\text{nd}}$ derivative} &\multicolumn{3}{c}{FPCA$_{Z=3}$} \\
& FPCR & FPLM$_{\text{G}}$ & FPLM$_{\text{L}}$ & FNP & FPLM$_{\text{G}}$ & FPLM$_{\text{L}}$ & FNP & FPLM$_{\text{G}}$ & FPLM$_{\text{L}}$ & FNP \\\toprule
\endhead
\hline \multicolumn{11}{r}{{Continued on next page}} \\
\endfoot
\endlastfoot
\hspace{.02in}{\underline{$t_5$}} \\
AMSE & 1.148 & 1.039 & 0.993 & 5.382 & 1.032 & \textBF{0.969} & 5.039 & 1.164 & 1.097 & 5.713 \\
AMSPE & 1.332 & 1.361 & 1.285 & 5.247 & 1.329 & \textBF{1.235} & 5.055 &1.541 & 1.452 & 5.484 \\
\\
\hspace{.02in}{\underline{Skewunimodal}} \\
AMSE & 1.600 & 1.237 & 1.216 & 5.847 & 1.148 & \textBF{1.136} & 5.353 & 1.337 & 1.320 & 6.182 \\
AMSPE &1.783 & 1.366 & 1.371 & 5.746 & 1.313 & \textBF{1.297} & 5.383 & 1.551 & 1.519 & 5.980 \\
\\
\hspace{.02in}{\underline{Skewbimodal}} \\
AMSE & 1.235 & 1.010 & 1.006 & 5.450 & \textBF{0.971} & 0.973 & 5.017 & 1.130 & 1.116 & 5.771 \\
AMSPE & 1.416 & 1.213 & 1.199 & 5.334 & \textBF{1.144} & 1.145 & 5.041 & 1.363 & 1.353 & 5.569 \\
\bottomrule
\end{longtable}
\end{center}

\vspace{-.2in}

Figure~\ref{fig:2} presents the log marginal likelihoods (LMLs) for the semi-metrics in all three error densities considered. Again, the semi-metric based on the second derivative has the largest LMLs and is thus considered the optimal semi-metric in this example.

\begin{figure}[!ht]
\centering
\subfloat[A global bandwidth]
{\includegraphics[width=7.9cm]{Fig_2a}\label{fig:2a}}
\qquad
\subfloat[Localized bandwidths]
{\includegraphics[width=7.9cm]{Fig_2b}\label{fig:2b}}
\caption{Comparisons of the LMLs in the functional partial linear model with a global bandwidth and localized bandwidths for the three choices of semi-metric. The semi-metric based on the first derivative is shown in white, the semi-metric based on the second derivative is shown in dark grey, and the semi-metric based on the FPCA is shown in light grey.}\label{fig:2}
\end{figure}

\subsubsection{Estimating the error density}

With a set of residuals and a fixed residual bandwidth, it is possible to apply a univariate kernel-density estimator and compute the discrepancy between $f(\varepsilon)$ and $\widehat{f}(\varepsilon)$ by using the following Monte-Carlo scheme:
\begin{itemize}
\item Compute 100 replications of residuals $\left[y_i^s-\widehat{g}_i^s(\cdot)\right]_{s=1,\dots,100}$;
\item Apply a univariate kernel density to estimate error density, where the residual bandwidth is estimated by the Bayesian method for 100 replications;
\item Compute the MISE and KL divergence between the true error density $f^s(\varepsilon)$ and estimated error density $\widehat{f}^s(\varepsilon)$ for $s=1,2,\dots,100$;
\item Obtain the AMISE and averaged KL divergence by averaging over 100 replications of MISE and KL divergence.
\end{itemize}

Table~\ref{tab:2} presents AMISEs and averaged KL divergences for the kernel error density with bandwidths estimated by Bayesian methods with a global bandwidth and localized bandwidths. For the three error densities, the kernel error density with localized bandwidths produces smaller AMISEs and smaller averaged KL divergences than the kernel error density with a global bandwidth.

\begin{table}[!htbp]
\centering
\tabcolsep 0.12cm
\caption{AMISEs and averaged KL divergences for the error-density estimation in the functional partial linear model with a global bandwidth and localized bandwidths for the three choices of semi-metric. The underscore G and L represent a global bandwidth and localized bandwidths for estimating error density. The smallest errors are highlighted in bold.}\label{tab:2}
\begin{tabular}{@{}llllllll@{}}\toprule
& \multicolumn{3}{c}{Type of semi-metrics (G)} & & \multicolumn{3}{c}{Type of semi-metrics (L)} \\
$f(\varepsilon)$ & $1^{\text{st}}$ derivative & $2^{\text{nd}}$ derivative & FPCA$_{Z=3}$ & & $1^{\text{st}}$ derivative & $2^{\text{nd}}$ derivative & FPCA$_{Z=3}$ \\\midrule
\underline{AMISE} \\
$t_5$ & 0.0015 & 0.0015 & 0.0019 & & \textBF{0.0008} & \textBF{0.0008} & 0.0008 \\
skewunimodal & 0.0088 & 0.0084 & 0.0088 & & 0.0074 & \textBF{0.0073} & 0.0075 \\
skewbimodal & 0.0026 & 0.0024 & 0.0026 & & 0.0024 & \textBF{0.0022} & 0.0026 \\
\\
\multicolumn{4}{l}{\hspace{-.13in} {\underline{Averaged KL divergence}}} \\
$t_5$ & 0.1427 & 0.1421 & 0.1957 & & 0.1299 & \textBF{0.1272} & 0.1391 \\
skewunimodal & 0.6205 & 0.5486 & 0.6737 & & 0.4996 & \textBF{0.4636} & 0.5695 \\
skewbimodal & 0.4247 & 0.3905 & 0.4736 & & 0.2990 & \textBF{0.2756} & 0.4112 \\
\bottomrule
\end{tabular}
\end{table}

\subsection{Diagnostic check}\label{sec:4.4}

As a demonstration with one replication, we plot the MCMC sample paths of the parameters on the left panel of Figure~\ref{fig:diag} and the autocorrelation functions (ACFs) of these sample paths on the right panel of Figure~\ref{fig:diag}. With the $t_5$ error density, these plots demonstrate that the sample paths are mixed reasonably well. Table~\ref{tab:diag} summarizes the ergodic averages, 95\% Bayesian credible intervals (CIs), standard error (SE), batch mean SE, and simulation inefficiency factor (SIF) values. Considered previously by \cite{KSC98} and \cite{MY00}, the SIF can be interpreted as the number of draws needed to have iid observations. Based on the SIF values, we find that the simulation chain converges very well.

\begin{table}[!bhtp]
\tabcolsep 0.27in
\centering
\caption{MCMC results of the bandwidth estimation under the prior density of IG$(\alpha=1,\beta=0.05)$ with $t_5$ error density.}\label{tab:diag}
\begin{tabular}{@{}llllll@{}}\toprule
\multicolumn{3}{l}{\hspace{-.255in}{Prior density: IG$(\alpha=1, \beta=0.05)$}} & SE & Batch-mean SE & SIF \\
Parameter & Mean & 95\% Bayesian CIs & & & \\\midrule
$h$ & 0.4656 & (0.2136, 0.7026) & 0.1217 & 0.3175 & 6.80 \\
$b$ & 0.5000 & (0.3377, 0.7078) & 0.0967 & 0.2300 & 5.65 \\\bottomrule
\end{tabular}
\end{table}

\begin{figure}[!htbp]
\centering
{\includegraphics[width=8.21cm]{Fig_3a}}
\quad
{\includegraphics[width=8.21cm]{Fig_3b}}
\\
{\includegraphics[width=8.21cm]{Fig_3c}}
\quad
{\includegraphics[width=8.21cm]{Fig_3d}}
\caption{MCMC sample paths and ACFs of the sample paths with $t_5$ error density.}\label{fig:diag}
\end{figure}

\subsection{Simulation of rough curves}\label{sec:rough}

In this simulation study, we consider the same functional form as given in~\eqref{eq:simu}, but add one extra variable $d_j\sim U(-0.1, 0.1)$ in the construction of curves. This functional form is taken from \citet[][Section 4.2]{Shang13b}. Figure~\ref{fig:rough} presents the simulated curves for one replication, along with the first-order derivative of the curves.
\begin{figure}[!htbp]
\centering
\subfloat[Raw functional curves]
{\includegraphics[width=8.5cm]{Fig_4a}}
\qquad
\subfloat[The first-order derivative of the curves]
{\includegraphics[width=8.5cm]{Fig_4b}}
\caption{100 simulated rough curves.}\label{fig:rough}
\end{figure}

From the smooth curves presented in Figure~\ref{fig:2}, we found the difference in LML between a global bandwidth and localized bandwidths to be quite small for the functional partial linear model. Therefore, in Figure~\ref{fig:Chib_rough}, we report only the LMLs for the functional partial linear model with a global bandwidth. The LMLs are computed for the three semi-metrics in all three error densities considered,  and the overall optimal semi-metric is determined based on 100 replications. With the median LML, the semi-metric based on the first derivative has the largest LML for the $t_5$ error density, followed closely by the semi-metric based on the FPCA with three retained components. In the skewunimodal and skewbimodal error densities, the semi-metric based on the FPCA gives the largest LML and is thus considered the optimal semi-metric in these two error densities.

\begin{figure}[!ht]
\centering
\includegraphics[width=13cm]{Fig_5}
\caption{Comparisons of the LMLs in the functional partial linear model with a global bandwidth for the three choices of semi-metric. The semi-metric based on the first derivative is shown in white, the semi-metric based on the second derivative is shown in dark grey, and the semi-metric based on the FPCA is shown in light grey.}\label{fig:Chib_rough}
\end{figure}

\section{Spectrometric data analysis}\label{sec:5}

This dataset focuses on the prediction of the fat content in meat samples based on near-infrared (NIR) absorbance spectra. The dataset was obtained from \url{http://lib.stat.cmu.edu/datasets/tecator} and has been studied by many researchers \citep[e.g.,][]{FV06, AV06}. Each food sample contains finely chopped pure meat with a percentage of fat content. For each unit $i$ (among 215 pieces of finely chopped meat), we observe one spectrometric curve, denoted by $\mathcal{X}_i$. The spectrometric curve measures the absorbance at a grid of 100 wavelengths, denoted by $\mathcal{X}_i=[\mathcal{X}_i(t_1),\dots,\mathcal{X}_i(t_{100})]$. For each unit $i$, we consider the first-order derivative of $\mathcal{X}_i$ and observe the fat content $y\in R$ by analytical chemical processing. Given a new spectrometric curve $(\mathcal{X}_{\text{new}}, \mathcal{X}^{'}_{\text{new}})$, we aim to predict the corresponding fat content $y_{\text{new}}$. A graphical display of the spectrometric curves is presented in Figure~\ref{fig:3}.
\begin{figure}[!ht]
\centering
\includegraphics[width=12.3cm]{Fig_6}
\caption{Graphical display of spectrometric curves.}\label{fig:3}
\end{figure}

To assess the point forecast accuracy of the functional partial linear model, we split the original samples into two subsamples \citep[see also][p.105]{FV06}. The first subsample is named the `learning sample', which contains the first 160 units $\{\mathcal{X}_i, \mathcal{Z}_i, y_i\}_{i=1,2,\dots,160}$. The second subsample is named the `testing sample', which contains the last 55 units $\{\mathcal{X}_l, \mathcal{Z}_l, y_l\}_{l=161,\dots,215}$. The learning sample allows us to build the regression model with the optimal smoothing parameter. The testing sample allows us to evaluate the prediction accuracy.

To measure estimation and prediction accuracies, we consider the root mean squared error (RMSE) and root mean squared prediction error (RMSPE). The errors are expressed as
\begin{align*}
\text{RMSE}&=\sqrt{\frac{1}{160}\sum_{\omega=1}^{160}\left(y_{\omega}-\widehat{y}_{\omega}\right)^2}, \\
\text{RMSPE}&=\sqrt{\frac{1}{55}\sum_{\delta=161}^{215}\left(y_{\delta}-\widehat{y}_{\delta}\right)^2}.
\end{align*}
For comparison, we also consider the functional principal component regression examined by \cite{RO07} and the functional nonparametric regression examined by \cite{FV06}.

As presented in Table~\ref{tab:3}, the functional partial linear model produces the smallest RMSE and RMSPE, in particular when the semi-metric is chosen based on the second derivative. The semi-metric based on the second derivative not only has the smallest RMSE and RMSPE, but it also has the largest LML.

\begin{table}[!ht]
\centering
\tabcolsep 0.6cm
\begin{small}
\caption{Estimation and forecast accuracies for the functional partial linear model, functional principal component regression, and functional nonparametric regression. The smallest error measures and largest LML are shown in bold.}\label{tab:3}
\begin{tabular}{@{}lc|cc|cc|cc@{}}\toprule
& & \multicolumn{6}{|c}{Type of semi-metrics} \\\cmidrule{3-8}
& & \multicolumn{2}{c}{$1^{\text{st}}$ derivative} & \multicolumn{2}{c}{$2^{\text{nd}}$ derivative} & \multicolumn{2}{c}{FPCA$_{Z=3}$} \\
Criterion & FPCR  & FPLM & FNP & FPLM & FNP & FPLM & FNP \\\toprule
RMSE & 8.0832  &  2.4281  & 4.6014 & \textBF{1.5993} & 2.2899 & 7.3236 & 10.8779 \\
RMSPE & 9.1156 & 1.9191 & 4.7755 & \textBF{1.4075} & 1.9429 & 8.3378 & 11.2603 \\
LML        & & -360.21                &         &     \textBF{-291.37}   &          &  -524.48 &  \\
\bottomrule
\end{tabular}
\end{small}
\end{table}

To verify the model adequacy, we present several scatter plots of the holdout responses against the predicted responses in Figure~\ref{fig:diag_2}. Among the three regression models, the functional partial linear model provides the best prediction accuracy.
\begin{figure}[!ht]
\centering
\includegraphics[width=\textwidth]{Fig_7}
\caption{Diagnostic check of the three functional regression models.}\label{fig:diag_2}
\end{figure}

The original functional data being iid allows sampling with replacement to obtain a set of bootstrap samples. For each bootstrap sample, we use the first 160 pairs of data for estimation and the remaining 55 pairs of data for assessing the prediction accuracy. By repeating this procedure 100 times, we obtain the averaged RMSEs, and RMSPEs presented in Table~\ref{tab:4}. The functional partial linear model produces more accurate forecasts than functional principal component regression and functional nonparametric regression. In particular, the functional partial linear model produces the most accurate forecasts when the semi-metric is based on the second derivative. This optimal selection of semi-metric is further confirmed by the boxplot of LMLs presented in Figure~\ref{fig:4}.

\begin{table}[!htb]
\centering
\tabcolsep 0.62cm
\caption{Estimation and forecast accuracy averaged over 100 replications for the functional partial linear model, functional principal component regression, and functional nonparametric regression. The smallest error measures are shown in bold.}\label{tab:4}
\begin{small}
\begin{tabular}{@{}lc|cccccc@{}}\toprule
& & \multicolumn{6}{c}{Type of semi-metrics} \\
& & \multicolumn{2}{c}{$1^{\text{st}}$ derivative} & \multicolumn{2}{c}{$2^{\text{nd}}$ derivative} & \multicolumn{2}{c}{FPCA$_{Z=3}$} \\
Criterion & FPCR & FPLM & FNP & FPLM & FNP & FPLM & FNP \\\toprule
RMSE  & 8.1011 &   2.2858  & 4.6449    & \textBF{1.5269} & 2.2343 & 7.3675 & 10.7080  \\
RMSPE  & 8.2234 &  2.3100 & 4.5655     & \textBF{1.6259} & 2.1947 & 7.8725 & 10.8047   \\
\bottomrule
\end{tabular}
\end{small}
\end{table}

\begin{figure}[!ht]
\centering
\includegraphics[width=12cm]{Fig_8}
\caption{Comparisons of the LMLs in the functional partial linear model with a global bandwidth for the three choices of semi-metric.}\label{fig:4}
\end{figure}

There has been rapid development in functional regression models. Here, we consider a large set of functional regression models collected in \cite{GS14} and \cite{FV11}. These models include:
\begin{inparaenum}
\item[(1)] restricted maximum likelihood-based functional linear model with a locally adaptive penalty \citep{CFS03};
\item[(2)] penalized functional regression \citep{GBC+11};
\item[(3)] functional principal component regression on the first few functional principal components \citep{RO07};
\item[(4)] linear model on the first $K$ functional principal components, where optimal $K$ is estimated by 20-fold bootstrap \citep{RS05};
\item[(5)] REML-based single-index signal regression with locally adaptive penalty \citep{Wood11};
\item[(6)] cross-validation based single-index signal regression \citep{ELM09};
\item[(7)] penalized partial least squares \citep{KBT08};
\item[(8)] least absolute shrinkage and selection operator penalized linear model on the first few functional principal components \citep{FHT10};
\item[(9)] functional nonparametric regression with NW estimator for estimating conditional mean \citep{FV06};
\item[(10)] functional nonparametric regression with NW estimator for estimating conditional median \citep{LLS11};
\item[(11)] functional nonparametric regression with NW estimator for estimating conditional mode \citep{FLV05};
\item[(12)] functional nonparametric regression with $k$ nearest neighbor estimator \citep{BFV09};
\item[(13)] functional nonparametric regression with most-predictive design points \citep{FHV10};
\item[(14)] functional partial linear model.
\end{inparaenum}

The boxplot of RMSPEs is presented in Figure~\ref{fig:spec_compar}. The functional partial linear model with the semi-metric and bandwidth selected by the Bayesian method has the smallest RMSPE among all methods considered.

\begin{figure}[!htbp]
\centering
\includegraphics[width=14cm]{Fig_9}
\caption{Comparisons of forecast accuracy for the 14 functional regression models listed above.}\label{fig:spec_compar}
\end{figure}

A by-product of the Bayesian method is that it is possible to compute the pointwise prediction interval nonparametrically. To make this computation, we first compute the cumulative density function of the error density, over a set of grid points within a range, such as between -10 and 10. Then, we take the inverse of the cumulative density function and find two grid points that are closest to the 10\% and 90\% quantiles. The 80\% pointwise prediction interval of a holdout sample is obtained by adding the two grid points to a point forecast. In Figure~\ref{fig:CI}, the holdout fat content in percentage is presented as diamond-shaped dots, the point forecasts of the fat content are presented as round circles, and the 80\% pointwise prediction intervals are presented as vertical bars. At the nominal coverage probability of 80\%, the empirical coverage probability is 87\%; at the nominal coverage probability of 50\%, the empirical coverage probability is 51\%.

\begin{figure}[!ht]
\centering
\includegraphics[width=14cm]{Fig_10}
\caption{A plot of predicted fat content in percentage and their 80\% pointwise prediction intervals. The actual holdout data are presented as diamond-shaped dots; the point forecasts of the fat content are presented as circles; the 80\% pointwise prediction intervals are presented as vertical bars.}\label{fig:CI}
\end{figure}

\section{Conclusion}\label{sec:6}

We propose a Bayesian method to estimate optimal bandwidths in a functional partial linear model with homoscedastic errors and unknown error density. As a by-product of the MCMC sampling algorithm, it allows us to compute log marginal likelihood for a semi-metric. The optimal semi-metric is the one that provides the smallest log marginal likelihood, as evident from the results in Table~\ref{tab:3}. Given that no closed-form expression for our bandwidth estimator exists, establishing the mathematical properties, such as the asymptotic optimality of \cite{Shibata81}, of the bandwidth estimator has been difficult. However, we have developed an approximate solution to the bandwidth estimator through MCMC. As a by-product of the Bayesian method, a prediction interval can be obtained, and marginal likelihood can also be used to determine the optimal choice of semi-metric among a set of semi-metrics.

Through a series of simulation studies, we find the functional partial linear model has better estimation and forecast accuracies than functional principal component regression and functional nonparametric regression. For a set of smooth curves, we further confirm the optimality of the semi-metric based on the second derivative; for a set of rough curves, we affirm the overall optimal semi-metric is the semi-metric based on the FPCA, followed closely by the semi-metric based on the first derivative. The kernel density estimator with localized bandwidths performs similarly to the kernel density estimator with a global bandwidth for estimating regression function and outperforms the one with a global bandwidth for estimating error density.

Using the spectroscopy dataset, the functional partial linear model produces the smallest forecast error of some commonly used functional regression models. The Bayesian method not only allows determination of the optimal semi-metric via marginal likelihood, but it also allows the nonparametric construction of pointwise prediction intervals for measuring prediction uncertainty.

There are many ways in which the Bayesian method and functional partial linear model can be extended, and we briefly outline five:
\begin{enumerate}
\item[1)] Combine different semi-metrics with weights based on their marginal likelihoods; this leads to the idea of ensemble forecasting.
\item[2)] Consider other functional regression estimators, such as the functional local-linear estimator of \cite{BFR+07} or the $k$-nearest neighbor estimator of \cite{BFV09} -- the functional local-linear estimator can improve the estimation accuracy of the regression function by using a higher-order kernel function; the $k$-nearest neighbor estimator considers the local structure of the data and gives better forecasts when the functional data are heterogeneously concentrated.
\item[3)] Extend to a functional partial linear model with heterogeneous errors; the covariate-dependent variance can be modeled by another kernel-density estimator \citep[e.g.,][]{CCP09}.
\item[4)] Extend to a functional partial linear model with autoregressive errors \citep[e.g.,][]{YZ06}.
\item[5)] Consider a $J$ test of \cite{DM81} for selecting non-nested functional regression models.
\end{enumerate}

\newpage
\bibliographystyle{apalike}

redpajama_set_name: RedPajamaArXiv


Once I finally had the pills in hand, dry skin was the side effect that impacted me the most day-to-day. My once oily face transformed into a desert. A light touch was all it took for the skin on my forehead to come off in flakes, and thin layers peeled off like an onion. Chapstick became a constant necessity. Even though I was always armed with something to soothe my cracked lips (I at least one stick in my backpack, another in my car, another in my bathroom, and others strewn about my bedroom) my lips remained unusually swollen and puffy. This was followed by nasal dryness that led to the occasional nosebleed.
Sulfur. In combination with other substances such as alcohol and salicylic acid, sulfur is a component of many over-the-counter acne medications. It usually isn't used by itself because of its unpleasant odor. It's unclear how sulfur works, but it has only a marginal benefit in most cases.
Acne is a common dermatological condition that affects most people at some stage in their life. Because acne is regarded as "normal" and over-the-counter products are readily available, most people will not seek treatment from their General Practitioner.
Jump up ^ Orion, E; Wolf, R (November–December 2014). "Psychologic factors in the development of facial dermatoses". Clinics in Dermatology (Review). 32 (6): 763–6. doi:10.1016/j.clindermatol.2014.02.015. PMID 25441469.
Comedonal acne: This type of acne is also caused by oil and debris clogging pores, but is characterized by skin-colored bumps called papules. These are typically found on the forehead or chin and are called "comodones," but are more commonly known as blackheads. They may either be closed, where the follicle is completely clogged, or open.
Patients are also required to participate in the iPledge online program. The program aims to prevent pregnancy by having patients confirm they understand the risks of the medication, promise to keep monthly appointments with their doctor, and agree not to share the medicine or donate blood while taking the drug. Each month, women must also answer a series of comprehension questions about birth control, and their prescribers must confirm results of a negative pregnancy test.
^ Jump up to: a b Arowojolu, AO; Gallo, MF; Lopez, LM; Grimes, DA (July 2012). "Combined oral contraceptive pills for treatment of acne". Cochrane Database of Systematic Reviews (Systematic Review & Meta-Analysis). 7 (7): CD004425. doi:10.1002/14651858.CD004425.pub6. PMID 22786490.


Karl (Den) - The Vault Fallout Wiki - Everything you need to know about Fallout 76, Fallout 4, New Vegas and more!
Quests Go to the Den and tell Karl it's alright to come back home.
Spare some change for (hic) an out-of-work farmer?
Karl is a former Modoc inhabitant, who fled to the Den from his farm. He can be found in Mom's Diner in Fallout 2.
An incredibly filthy drunk, Karl spends his days moping in the back of Mom's diner, begging passers-by for money to fuel his drinking habit. He used to be a fine, upstanding farmer from Modoc, who worked a farm to the northeast of the town. However, one day he began seeing glowing ghosts in the fields, who took his crops and cattle. Eventually, he couldn't take the stress and run away from the farm. He is presumed dead by Modoc citizens.
Jo is suspecious of the Slags. Find out about the dead bodies at the Ghost Farm and find out what happened to Karl. and Go to the Den and tell Karl it's alright to come back home.: Talking to Karl and learning about his story is necessary for peacefully resolving the dispute between Modoc and the Slags. Once that is accomplished, the player can tell Karl that they can come home.
Karl can become upset if the player offers him Nuka-Cola, mocks him, or gives him too little money. In that case, he will refuse to tell his story, making it impossible to complete the above quests peacefully or learn his story in advance. In this case, the player will have to apologize and give him $100, a beer, or booze.
Of course, giving him any kind of alcohol will cause him to pass out for a few hours.
Female characters can sleep with Karl if they have 8 Charisma. The surprisingly enjoyable romp is worth $1000.
Karl appears only in Fallout 2.
Quests Sabotage Becky's still. · Get car part for Smitty. · Return Anna's locket. · Collect money from Fred. · Get book from Derek. · Deliver a meal to Smitty for Mom. · Lara wants to know what is being guarded in the church. · Get permission from Metzger for gang war. · Find weakness in Tyler's gang guarding the church. · Help Lara attack Tyler's gang. · Listen to Stacy's kitty story · Find Vic the Trader.
This page was last edited on 23 October 2018, at 23:08.


Horizon Technologies has released a new version of its FlyingFish 3 Airborne Satphone monitoring product: FlyingFish 3/SI which monitors Iridium Satphones from manned and unmanned airborne platforms.
The new Iridium module monitors and intercepts voice, SMS, call data (2.4 Kbps), Short Burst Data (SBD) service, Iridium pager and the location of Iridium Satphones within line-of-sight of the aircraft. The system monitors both uplink and downlink signals so both sides of the call can be monitored (depending on interception conditions). All captured sessions and related data are stored in our database for offline analysis and playback. The Graphic User Interface of our new FlyingFish Tactical Interface (FTI) software is very user-friendly and displays the position of Iridium Satphones on the map together with the Thuraya and ISatPhone Pro Satphone locations.
The FlyingFish 3/SI product can be procured stand alone or as an upgrade kit to our FlyingFish systems deployed in the field.


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In Andy Reid Era Philadelphia Eagles Assistants Key to Success
Published by Chris Murray on May 27, 2009
In the last 10 years, under Andy Reid's tenure as head coach, the Philadelphia Eagles have made seven trips to the postseason that included five NFC Championship games, five NFC East titles, and one Super Bowl appearance.
Another sign of the Eagles success in the Reid era is that several of his coaches have moved on to other teams as head coaches or coordinators.
Three of Reid's former assistants led teams to the playoffs in 2008—Minnesota Vikings head coach Brad Childress (offensive coordinator), Baltimore Ravens head coach John Harbaugh (special teams coach), and Steve Spagnuolo, who is the new head coach of the St. Louis Rams, helped lead the New Y...
Kobe Bryant: A Hero By Definition
ECF Cavs-Magic: Last Two Games Are Why People Don't Watch NBA Games
Bucs GM Mark Dominik: DUMB OR STUPID?
Pittsburgh Steelers Offense to Be "Sweeder" in 2009
Phillies-Dodgers: Hamels Does Hollywood in Shutout Win

redpajama_set_name: RedPajamaCommonCrawl


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Le Bioparc Valencia est un parc zoologique espagnol situé en Communauté valencienne, au sein du quartier Sant Pau de Valence, dans la continuité des jardins du Turia et du parc de Cabecera. Fondé en 2008, il a remplacé le Jardin zoologique de Valence, qui était situé dans les . Il est la propriété de la municipalité de Valence, mais est exploité par une société privée, Rain Forest Valencia, qui gère aussi le Bioparc Fuengirola, en Andalousie.

Sa superficie couvre , sur lesquels sont présentés plus de 800 animaux de 116 espèces. Spécialisé dans la faune africaine, il est divisé en quatre zones représentant quatre biomes : savane sèche, savane humide, forêt équatoriale et forêt tropicale malgache. Réalisé par la société Rain Forest Diseño, il a été pensé de manière à cacher les barrières entre le public et les animaux afin de donner au visiteur la sensation d'entrer dans l'habitat de l'animal, suivant le concept d'immersion.

Membre permanent de l'Association européenne des zoos et aquariums, il s'engage dans la conservation ex situ en participant à des programmes européens pour les espèces menacées (EEP). Il soutient également des actions de conservation in situ œuvrant sur le terrain à travers son organisme dédié, la Fondation Bioparc.

En 2014, il a accueilli  visiteurs.

Historique

Ouverture
De nombreux animaux du Jardin zoologique de Valence (1965-2007) ont été transférés dans le Bioparc lors de sa création, comme les hippopotames amphibies, les chimpanzés, les lions, les girafes et les canards.

Années 2010

Installations et faune hébergée
En 2016 il présente environ 830 mammifères, oiseaux et reptiles.

Savane sèche
C'est la plus grande des quatre zones du parc. Une plaine africaine expose principalement des girafes de Rothschild, des zèbres de Grant, des autruches, des impalas, des gazelles de Thomson et des rhinocéros blancs du sud. Un groupe de huit éléphants de savane d'Afrique prend place dans un espace adjacent.

Des prédateurs sont aussi présentés dans cette zone avec les lions d'Afrique et les hyènes tachetées.

Une partie de cette zone permet de découvrir les animaux vivant sous terre ou dans des grottes. On peut notamment y voir des oryctéropes, des porcs-épics, des rongeurs et des serpents.

Savane humide
Cette petite zone présente un groupe d'espèces typiques de ce biome. Une installation inspirée de la grotte de Kitum, un site naturel kényan, permet d'observer des hippopotames amphibies, des crocodiles du Nil et des poissons endémiques des rivières et des lacs africains (Tilapias, Aulonocara et Nimbochromis), en vision subaquatique.

Des spatules africaines, des pélicans, des tortues molles du Nil et des amphibiens sont également présentés.

Forêt équatoriale
Dans cette zone sont notamment présentés des primates, dont deux espèces de grands singes, chimpanzés et gorilles des plaines de l'ouest, ainsi que des drills, des cercopithèques de Brazza, des talapoins et des mangabeys couronnés.

Les gorilles sont divisés en deux groupes, un groupe reproducteur comprenant un mâle, trois femelles et leurs éventuels petits, et un groupe de trois mâles solitaires : Jitu (1983), Thomas (2002) et Kabuli (2004). Le mâle reproducteur, Mambi, et une des femelles, Ali, ont donné naissance à un premier jeune, Ebo, en 2012. Mambi a également engendré un second jeune en 2016, Virunga, avec la femelle Nalani, et un troisième en 2017, Mbeli, avec Ali.

Un enclos permet la présentation de trois panthères du Sri Lanka (une sous-espèce asiatique du léopard, proche des sous-espèces africaines) : un couple reproducteur et une femelle mélanique hybride stérilisée. Un espace aquatique présente des hippopotames nains.

Un autre enclos présente des bongos.

Madagascar
Cette zone comprend l'enclos des fossas et un espace dédiés aux lémuriens, que les visiteurs peuvent traverser. Les espèces de lémuriens présentées sont les lémurs catta, les lémurs à ventre roux, les lémurs à front roux, les lémurs mongos, les varis noirs et blancs et les varis roux.

Conservation

Le parc s'investit dans la conservation à travers la Fondation Bioparc. Elle soutient notamment un programme de conservation de la forêt d'Ebo au Cameroun, où vivent des gorilles.

Économie

En 2014, il a accueilli  visiteurs.

Notes et références

Notes

Références

Voir aussi

Parc ou jardin public à Valence (Espagne)
Parc zoologique en Espagne

redpajama_set_name: RedPajamaWikipedia


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Billie Eilish's Dream Comes True With Justin Bieber Song Collaboration
Billie Eilish's childhood fantasy has come true. The pop sensation teamed up with longtime crush Justin Bieber for a remix of her smash single "'Bad Guy," and announced the news with an instantly-iconic throwback post. The song's cover art proves that Billie's fandom for the "Sorry" singer is the real deal and always has been, but she'd already made her feelings clear for years!


ExercisABILITIES was founded to be a place for the Southeast MN community to have improved access to rehabilitation services. Our highly skilled physical therapy staff are specialists in treating most community based issues. Research and experience shows that movement is one key to improved health. We will help you regain movement, decrease pain, and achieve overall good health again. These specialty issues include diagnoses that range from chronic pain/fibromyalgia to senior balance issues to any neurologic issue. Please see the Pediatric Rehabilitation Page for details for children.
Our business office will research your coverage and notify you of your responsibility prior to your evaluation. Co-pays and Deductibles will be collected at time of service. All insurance covered is dependent on qualifications for skilled need for care. Your physical therapist can discuss this with you.
Call your physician's office for a referral or request one on your portal. Not all insurances require a referral but we do prefer you start with a referral since most insurances do require this. Call us if you have difficulty getting a referral and we can discuss. MN state laws do not require a provider referral to initiate physical therapy.
Call us to initiate intake. We will need your demographic information and a photocopy of your insurance card. You can print and fax or drop by the intake form below.


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Q: C++ pointers, intitializing objects, etc I am new to C++ and am curious..
Why does this compile but crash at runtime:
 wxBitmap *bmp;
*bmp = wxNullBitmap;   //wxNullBitmap is type wxBitmap with null data

when this would compile and run fine:
  wxBitmap bmp;
  bmp = wxNullBitmap;

Isn't it the same thing??

A: Pointer is address of memory. In first example, you create pointer but it's value is undefined. Where does it point to? And then you try to copy your objects to some random, undefined location in memory. OS doesn't let you to do it.

redpajama_set_name: RedPajamaStackExchange


Crafters of all skill levels will use these designs to create beautiful, fanciful flowers to wear and use to embellish their handicrafts. A collection of innovative projects—including lanterns, a necklace, a bag, gloves, and a fabulous wedding dress—rounds out this beautiful book.
This eagerly awaited follow-up to the best-selling Nicky Epstein's Knitted Flowers will inspire crafters everywhere. The indomitable Nicky Epstein does for crocheters what she did for knitters: provide a collection of exquisite flowers to craft. Small, simple and time-efficient, flowers are the perfect project for crocheters who want some instant gratification. The best part? These flowers will last forever.


text:
Q: Using promise() to run next function doesn't work - PLAIN JAVASCRIPT I'm very new to Javascript development.
PROJECT -
I'm currently working on a web chatbot application.
PROBLEM -
I'm not able to use the promise() function to run more than one function one after another.
CODE -
var messages = [
  `Hello name`,
  `I'm hosting a party on Sunday at my house, for my birthday`,
  `I'll be really happy if you'd come`,
];

chatWindow = document.querySelector(".message-day");

const startChat = () => {
  return new Promise(function (resolve, reject) {
    messages.forEach((message) => {
      setTimeout(() => {
        chatWindow.innerHTML += `

Karan

                 ${message}

                  9:12am

 `;
      }, 2000);
    });
    resolve();
  });
};

startChat().then(() => {
  console.log("2nd Functions");
});

You can also see the code live here
How do I get the 2nd function to run after the startchat()[the first function] ends.

A: Now you return 1 promise for 3 operations but it looks like you meant to make all 3 operations async. To achieve this, you need to return a promise, for each async operation.
You might be looking for something like this:
const messages = [
  `Hello name`,
  `I'm hosting a party on Sunday at my house, for my birthday`,
  `I'll be really happy if you'd come`,
];

const chatWindow = document.querySelector(".message-day");

const startChat = () => messages.map(
    // Returns array of promises wrapping
    // each message into a promise
    (message, index) => new Promise(resolve => {
        setTimeout(() => {
            chatWindow.innerHTML += `

Karan

                     ${message}

                      9:12am

`;
            resolve(message);
        }, 2000 * index);
    })
);

Promise.all(startChat())
    .then(args => {
        // args will contain same strings as messages
        console.log("2nd Functions", args);
    });

If you would like to invoke a callback before/after each message is printed, I'd suggest to pass the callback as an argument to startChat & invoke it when needed.


text:
Tag Archives: big in Japan
Bad Reputation (2018)
Joan Jett is a rock and roll icon.
(2018) Music Documentary (Magnolia) Joan Jett, Kenny Laguna, Iggy Pop, Billy Joe Armstrong, Michael J. Fox, Deborah Harry, Chris Stein, Kathleen Hanna, Miley Cyrus, Ian MacKaye, Pete Townshend, Bill Curbishley, Mike Ness, Kristen Stewart, Dougie Needles, Alison Mosshart, Dana White, Sally Hershberger, Rodney Bingenheimer, Thommy Price, Carianne Brinkman, Cherie Currie. Directed by Kevin Kerslake
One of the problems we film critics have is that often with documentaries we have a tendency to review the subject as much as the film. I'm certainly guilty of that and the temptation to do that with an icon like Joan Jett is damn near irresistible.
You can't help but admire Jett as a musician. In an age when most women were relegated to playing soft rock or folk music, Jett wanted to rock hard. She wanted to be like the boys onstage; like Pete Townshend, like Jimmy Page, like Clapton. People in the industry would look at her like she was from Mars. Girls don't rock; they strum. They sing sweetly and they certainly don't shriek
As a teen, Joan Larkin made her way from Pennsylvania to Los Angeles to chase her rock and roll dreams. She hung out in the English Disco, an all-ages nightclub where glam rock was worshiped by men and women wearing way too much make-up. Joan stood out in that crowd and met Sandy West, a kindred spirit who wanted to be John Bonham. They added guitarist Lita Ford, singer Cherie Currie and bassist Jackie Fox and were christened The Runaways. Joan took her mother's maiden name as her stage name and under the aegis of promoter Kim Fowley (whom Iggy Pop described as "like Frankenstein's monster, if Frankenstein's monster was on Quaaludes") they would go on to record four studio albums and one live album before breaking up acrimoniously.
The band was met by critical scorn and by outright hostility by male rockers who didn't want to see their clubhouse invaded by girls yet performance footage (of which there is sadly far too little) show that the Runaways were as hard rocking as any male band of their time. When the band broke up, Jett was devastated. She self-medicated with booze and drugs, hanging out with people like Sid Vicious, Nancy Spungeon and Stiv Bators, most of whom as Jett puts it "are dead now." She even thought of joining the military to get herself straightened out but it was rock and roll that saved her.
She was introduced to Kenny Laguna, a noted bubblegum pop producer who heard something in Jett. Putting together a backing band who became known as the Blackhearts, Laguna melded his pop sensibilities with Joan's hard rock instincts to create a kind of hard pop. When no label would even consider them, Jett and Laguna founded heir own label, becoming a precursor to the DIY punk labels that started in the 80s. When pop mogul Neil Bogart heard their demo, he arranged to distribute their first album and it looked like a wise move when the first album did extremely well but Bogart died before they could follow up on that success and his label died with him. Undaunted, the band found another label to distribute their music and they hit the big time powered by constant airplay on MTV. While most of the band's hits were covers ("I Love Rock and Roll," "Crimson and Clover") there were several that Jett and Laguna penned as well ("Bad Reputation"). Through the 80s, Jett became the Queen of Rock, a darker haired version of Ann and Nancy Wilson.
The rock business has always been notoriously cyclical and as label relationships soured, the Blackhearts were bounced from label to label but while Jett and her band would never recapture the popularity they had in the 80s they continued to have hits here and there through the 90s and into the 21st century.
Now so far I've reviewed the subject and certainly Jett is worthy of a documentary but the problem with this documentary is a lack of depth. It's a bit more of a puff piece and Kerslake doesn't seem inclined to examine some of the darker subjects, like the allegations in Cherie Currie's book that Fowley had sexually assaulted members of the Runaways – Jett is certainly aware of those allegations and you'd think in this MeToo era she would be at least wanting to comment on them, even if only to say "I wasn't aware of that kind of thing going on so I can't validate Cherie's story."
There is also astonishingly little detail in how the high school aged Joan got from Pennsylvania to the West Coast, whether she was able to reconnect with her former bandmates in the Runaways or even who her personal influences are as a musician. Watching this movie is very much like staring at a picture that has been put through a shredder and tossed in a trash can and then later reassembled at the city dump; there are lots of pieces missing and the ones that are there are incomplete.
Still, Jett is candid and engaging. She doesn't address her sexuality – I don't think she should have to – which has been a subject of gossip for decades. If anything, I think Jett is married to rock and roll and that's the source of her sexuality and her creativity. It is her center and her savior, and often her curse. It is the greatest love in her life. And like all of our own relationships it has had its ups and downs but she is still loyal to it nevertheless. That's pretty damn admirable if you ask me.
You likely won't respect Jett as a musician any more after seeing this than you already do – or do not, if you are of that mindset. You may find yourself respecting her more as a person as I did. Overall I'd have to say that while Jett is indeed a rock icon who deserves every accolade she gets thrown her way, I might have wished for a better biography of her than this. She's earned better.
REASONS TO GO: Jett is a marvelous subject; she's candid and engaging.
REASONS TO STAY: A little bit Music Documentary 101.
FAMILY VALUES: There's some brief nudity, sexual references and gestures, profanity and drug references.
TRIVIAL PURSUIT: Jett celebrated her 60th birthday just four days before the film was released.
BEYOND THE THEATERS: Fandango Now, Google Play, iTunes, Microsoft, Vudu, YouTube
COMPARISON SHOPPING: The Runaways
NEXT: Matangi/Maya/M.I.A.
Posted in New Releases, VOD Review	| Tagged Bad Reputation, big in Japan, Billy Joe Armstrong, Bruce Springsteen, Cherie Currie, Chris Stein, cinema, Cinema365, cover versions, Deborah Harry, English Disco, Films, Ian Mackaye, Iggy Pop, Joan Jett, Kathleen Hanna, Kenny Laguna, Kim Fowley, Kristen Stewart, Light of Day, Los Angeles, Magnolia Releasing, Mia Zapata, Michael J. Fox, Mike Ness, Miley Cyrus, misogyny, movies, music documentary, Neil Bogart, New York City, Pete Townshend, rape allegations, reviews, Rock and Roll Hall of Fame, Rodney Bingenheimer, sexuality, The Gits, The Runaways, VOD Reviews	| Leave a reply
The Runaways
Joan Jett loves rock and roll; Cherie Currie loves the lifestyle.
(2010) Musical Biography (Apparition) Kristen Stewart, Dakota Fanning, Michael Shannon, Danielle Riley Keough, Scout Taylor-Compton, Tatum O'Neal, Stella Maeve, Brett Cullen, Alia Shawkat, Johnny Lewis, Hannah Marks, Jill Andre. Directed by Floria Sigismondi
The world of rock and roll is a harsh one, full of broken promises and shattered dreams. Every so often, a performer or a band will break through and change things; on other occasions, a performer or a band will succumb to the excesses of the industry. Sometimes, a performer or a band will do both.
Joan Jett (Stewart) is a young girl who idolizes Suzi Quatro and Keith Richards. She's an adept guitarist but nobody will take her seriously and she longs to be in a rock and roll band. She meets Kim Fowley (Shannon), a fixture on the Sunset Strip in the 1970s-era Los Angeles when this all took place. Fowley sees himself as an acute judge of talent and a canny promoter who understands what sells. He longs to be a major player in the music business, something he is not at the time. He likes Jett's look and her dream of fronting an all-woman rock band – there were none at the time that had any success, although in pop music the girl groups of the 60s (Martha and the Vandellas and over in Motown the Supremes) had met with success. However, these were women who projected a certain safe and virtuous image. Fowley – and Jett – wanted danger and subversion. Fowley hooked up Jett with Sandy West (Maeve), a drummer. The two began practicing together but the band needed fleshing out.
Cherie Currie (Fanning) is Bowie-obsessed and performs one of his songs dressed just like him at a school talent show, getting booed by her audience and flipping them off in retaliation. Her home life is falling apart at the seams – her dad (Cullen) is an alcoholic, spiraling slowly to an inevitable end and her mom (O'Neal) has fled to Indonesia to escape, leaving her with her twin Marie (Keough) as essentially sole support. Fowley discovers her and brings her to his trashy trailer to perform with the band. At first Cherie is stiff and hesitant but with Fowley pushing her/abusing her into the right attitude, her natural performing talent, sexuality and charisma come to the fore. "It's not women's lib," Fowley crows, "Its women's libido!" The remaining spots in the band are filled up with guitarist Lita Ford (Taylor-Compton) and bassist Robin Wolf (Shawkat).
The group plays a series of gigs in a series of depressing dives before Fowley gets them signed to a major label. A song, "Cherry Bomb" becomes a minor hit (although it becomes a big one in Japan) and the band begins to headline gigs and support major acts in stadiums. They go to Japan where they are mobbed by rabid fans and all of a sudden this group of young girls – all in their mid-teens at the time – suddenly are cursed with the success of the rock and roll lifestyle; plenty of sex, plenty of drugs, and not so much rock and roll. Eventually, the curse of success will overcome the band, with internal musical differences and Currie's drug habit proving to be too much for the band to survive.
Director Sigismondi makes her feature debut here after mostly directing music videos, as well as working in fine arts (she's a talented photographer and sculptor as well) and to her credit she makes the most of a very little. She manages to capture the look and feel of both the L.A. suburbs in the 70s (I should know – that's where I lived at the time) and the decadent scene on the Sunset Strip.
I've been a big fan of Fanning for a long time and she doesn't disappoint here. She captures the nature of the vulnerable and sometimes lost Currie nicely, showing her as clay to be molded by Fowley and drifting off-course, prey to the temptations of the road. As her family life disintegrates, she becomes more and more lost. The movie to a large extent focuses most on Currie (but to be fair, she did write the biography that the movie is based on) and Fanning handles the load nicely.
Stewart, best known as the angst-ridden Bella Swan in the Twilight franchise is surprisingly rough-edged here, showing the force-of-nature strength of Jett but also her bisexual tendencies. There is a fairly lurid make-out scene between Jett and Currie which comes off as exploitative, but given the nature of the band and the era, kind of makes sense as something like it would appear in a 70s "B" movie, which this closely resembles in tone. Stewart shows more range here than she has previously, forcing me to revise my opinion of her as a somewhat one-note actress. I look forward to seeing more from her along these lines.
Shannon is a terrific actor who has one Oscar nomination to his credit and has the chops to garner more of the same should he get the right roles. This one is not, but he does capture the manic and manipulative nature of Fowley who yearned to be a mover and a shaker, but whose claim to fame would always be this band. He often claimed he assembled the Runaways both conceptually and practically, a claim he has backed off from in recent years. Shannon is riveting in the part, capturing both the yin and the yang of Fowley who could be supportive one moment and abusive the next.
In fact, in many ways this movie sugarcoats the Runaways story, leaving out allegations of sexual and physical abuse around the band. It also leaves out the backstory of the rest of the band (in the case of Ford, at the real Lita's request) in focusing on the two leads. The filmmakers do a disservice to the band in essentially portraying them as a two-woman creative team (in reality, West and Ford co-wrote most of the songs with Jett and Fowley). While it's true Jett and Currie were the heart and soul of the band, it would have been nice to include more of the rest of the band's story in the movie, particularly that of West who passed away from lung cancer just prior to the beginning of filming.
The legacy of the Runaways is undeniable; Joan Jett remains a rock and roll icon, an inspiration to young female rockers everywhere. It's a bit of a crying shame that they remain largely unknown here and those who do know them mostly know them for "Cherry Bomb," their signature hit. They were certainly much more than that, and anyone who has seen their Showtime documentary (which includes some incendiary performance footage) will attest to that. The movie picks up part of their essence – enough to make it worth seeing. I just wish we would have gotten a little bit more of it.
WHY RENT THIS: An authentic recreation of the time and the scene. Surprisingly gritty performances from Stewart and Fanning. Shannon shows a good deal of charisma.
WHY RENT SOMETHING ELSE: The movie leaves out a good deal of information, and fictionalizes or trivializes the group's achievements.
FAMILY VALUES: There are occasionally graphic depictions of teen sex and drug use, as well as a whole lot of foul language.
TRIVIAL PURSUIT: Jackie Fox, the actual bass player for the Runaways, declined to give the producers of the film the rights to her life story so a fictional character was introduced to be the Runaways bassist (and ironically, has no lines in the film); Lita Ford also declined to give her rights to the producers, but did meet with Scout Taylor-Compton prior to filming and declared that even if the film was awful, Taylor-Compton at least did her character justice.
BOX OFFICE PERFORMANCE: $4.7M on a $10M production budget; the movie was a flop.
TOMORROW: A Single Man
Posted in DVD Review	| Tagged 70s, Apparition, big in Japan, biopic, bisexuality, Cherie Currie, Cherry Bomb, cinema, Dakota Fanning, DVD Reviews, dysfunctional family, Films, Joan Jett, Kim Fowley, Kristen Stewart, Los Angeles, Michael Shannon, movies, musical biography, rock and roll, Scout Taylor-Compton, sex drugs and rock and roll, Sunset Strip, Svengali, talent show, Tatum O'Neal, teenage sex symbols, The Runaways	| Leave a reply


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Our pressure is working! The UK Prime Minister just urged the Saudis to stop Ali's execution. But Germany and the US have yet to speak out. Send an urgent message.
Saudi Arabia is about to behead a 21-year-old man and then crucify his body in public. This same country was just chosen to head a UN Human Rights Council panel. What staggering hypocrisy!
Ali Mohammed al-Nimr was arrested when he was 17 for participating in demonstrations against the government, then he was convicted under torture. But his case is not an exception — Saudi Arabia has executed more than 100 people this year, that's a rate of one every two days!
Saudi is now Chair of the UN committee that oversees nominations to key special rapporteurs and experts. Ali's whole atrocious case shows how absurd that is! Human rights experts say this is an 'arbitrary execution' prohibited under the international Convention on the Rights of the Child, as Ali would be executed for crimes committed when he was a minor. But they will go ahead unless there is a massive cost on the international stage.
The US and Germany have an ugly, but tight trade relationship with Saudi — they either sell the Kingdom weapons or buy oil, or both! We know international voices count. When we campaigned earlier this year for the German Vice Chancellor to tell Saudi officials to stop the flogging and possible execution of the blogger Raif Badawi, Sigmar Gabriel spoke out. Badawi hasn't been flogged since and he's still alive. He is still rotting in prison.
When regimes worldwide violate basic human rights, our community has spoken out and helped stop atrocities. Let's now come together for Ali.


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One Direction's 'One Way Or Another': Boy Band's Charity Cover Leaked (AUDIO)
The boys of One Direction have gone all retro on us, recording a cover of Blondie's smash hit, "One Way or Another."
The boy band recorded the cover to support UK charity Comic Relief, which uses entertainment to raise money to take on poverty and social injustice. One Direction is scheduled to perform the song at the Brit Awards on Feb. 12.
The full "One Way or Another" cover was set to debut later this month, but a low-quality recording of the song leaked this week -- take a listen above.
1D's Louis Tomlinson took to his Twitter account on Tuesday to ask fans to pre-order the track, saying that it is "very sad to see" that the cover was leaked.
I hear the charity single has been leaked. Very sad to see. Don't forget together we are trying to raise money for comic relief.
— Louis Tomlinson (@Louis_Tomlinson) February 5, 2013
Please get behind an incredible charity and make a real difference. You can pre order now from iTunes for the official track. Thank you
A Beginner's Guide To One Direction's Tattoos
One Direction Comic Relief 1 D Entertainment
Although Liam doesn't have any tattoos himself, he says he isn't opposed to them entirely. His girlfriend Danielle Peazer has one on her wrist.


This business list of senior decision makers and administrators in the health services and hospitals includes public and private hospitals, area health services, clinics and government departments.
This business list reflects in detail Australia's health services and health related government departments, bodies and services.
The Health Services & Hospitals Decision Makers list is sourced from the A-Z GovBIZ database.


text:
Deputy PM Phạm Bình Minh meets Moroccan official
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Deputy Prime Minister and Foreign Minister Phạm Bình Minh received Moroccan Secretary of State to the Ministry of Foreign Affairs and International Cooperation Mounia Boucetta on Tuesday.
Boucetta is visiting Việt Nam to co-chair the fourth meeting of the Việt Nam – Morocco Joint Committee and the fifth political consultation between the two foreign ministries.
Hailing the development of bilateral cooperation in all fields, Minh praised Morocco's efforts to deepen relations with members of the Association of Southeast Asian Nations (ASEAN), with a view to becoming its Sectoral Dialogue Partner. He said the two countries should increase the exchange of delegations at all levels.
The two officials stressed the need to take practical measures to foster trade and investment ties, increase the exchange of business delegations to explore each other's markets, and develop economic ties with other African countries.
Việt Nam welcomed Morocco to open its honorary consulate in HCM City in a bid to boost economic and trade cooperation with Việt Nam's southern provinces and cities.
The two sides agreed to grant more scholarships to their students, increase the exchange of researchers, hold more academic workshops and sign agreements between research institutions.
Alongside this, the two countries are set to accelerate negotiations and sign cooperation deals in other fields such as labour, finance-banking, tourism, aviation, and renewable energy.
At the meeting, Minh also lauded the signing of the memorandum of understanding on cooperation between Việt Nam's Ministry of Labour, War Invalids and Social Affairs and Morocco's Ministry of Employment and Social Affairs and the establishment of the Việt Nam – Morocco Friendship Association.
He also suggested stronger cooperation between two countries' localities like Nha Trang-Agadir, HCM City-Casablanca, and Đà Nẵng-Tangier.
During the political consultation, the two sides also discussed regional and international issues of mutual concern
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gPotato and Astrum Nival have responded to the community outrage over the recent Allods Online changes.
Over the last several days, the Allods team has been spending a lot of time listening to player feedback. We've noticed that two of the biggest topics this weekend have been regarding rumors of Astrum Nival remaining as the developers for Allods and what our future plans are for the item shop. We wanted to take a moment to address these topics and clear up some of the general questions many of you may have.
The original Astrum Nival developers are no longer involved in Allods!
The original development team for Allods Online is still 100% involved in developing Allods.
To provide everyone insight on the situation let's take a trip down memory lane. The developers for Allods Online were originally known as Nival Online. On July 6th, 2009 Nival Online merged with Astrum Online Entertainment and became what most people know them as, Astrum Nival. Then on December 1st, 2009, Mail.ru merged with Astrum Online Entertainment. Astrum Online Entertainment operates Astrum Nival, the development studio which developed our beloved game, Allods Online.
In any case, the original developers are intact – they just have a new company name. The original vision of Allods Online is still being followed by the developers. Allods Online is in great hands and is being actively developed!
Item shop prices are overpriced, what is gPotato doing about this?
As we mentioned in our official statement last week, the Allods team is well aware of the situation. We can't apologize enough for the stir and shock it's caused within the community and the lack of communication we had beforehand with not evolving you, the players, in our decision making process.
We want to make clear that this is something we are not taking lightly. We are not sitting and waiting just to see how many dollars we're going to make over the next four weeks. It is very clear to us that players are already disgruntled with the situation and we are actively working on new pricing options to accommodate the masses. However, we ask the Allods community to please be patient with the situation! Adjustments like this cannot happen overnight. That's why we continually encourage everyone to submit constructive feedback to us regarding your opinion about both the game and the item shop. In fact, we started a forum thread that we will be checking on an hourly basis here.
The Allods team works hard on this game and loves it just as much as many of you do. When we see a problem we want to address it and take the most appropriate actions that make sense for both the players and the game. With that said, we encourage everyone to voice your opinion, even if it's about something you absolutely hate, just please do so in a constructive manner.
Thank you everyone for your continued support! As we've said many times, the Allods fans are some of the best gamers in the world – we really appreciate that!
First, they dispelled the conspiracy theory that the original developers were gone. Still, that is a lot of merging and there are reports out of Russia that mail.ru is a less than reputable online-games operator.
The price hike in the cash shop does not appear to have been a mistake as first assumed (they literally multiplied the prices by 10 for everything which made it seem like an obvious mistake).
The changes to Fear of Death, mana/health regen, and leveling speed are not addressed in the post directly, but are the catalyst of the problem. I sincerely hope that Astrum Nival and gPotato realize the prices aren't the problem, its them crippling the game to force players into the cash shop. The cash shop should be about convenience, not necessity.
They have brought up a forum thread to collect feedback.


As we've seen in mass torts cases, there's usually a slow rise in potential cases as the word gets out about the nature of the case - and people start realizing their problems weren't just normal side effects, but were the result of negligence - followed by a big wave of claims as television advertising and the like kicks in, and thereafter a slowing number of claims that eventually becomes a trickle.
Often, the reason for this "wave" of claims is due to the defendant's actions: the defendant recalls the product in question, so it's not longer out in the market and so can't hurt anyone. That, for example, is how Vioxx worked: when Vioxx was recalled, it wasn't out on the market anymore.
The DePuy hip implants, however, are still in people's hips and still failing at an alarming rate. Thus, product liability lawyers like us have continued to see a steady stream of potential clients, many of them people who saw the big rush of lawyer advertising, and some of whom even know someone else with a failed implant, but who didn't think they would need a lawyer themselves - until their implant failed, and they were told to have a revision surgery. That's when they started looking for a lawyer, considering a lawsuit, and wondering about potential compensation.
These later clients are usually quite savvy. They've spent a fair amount of time on the internet researching the subject, but they haven't been able to answer one of the key questions they're considering when trying to decide whether or not to bring a lawsuit: how much do DePuy hip implant patients get in a settlement? I can understand their frustration; for all the information on the Internet put out by DePuy lawyers, nobody talks about how much the cases are worth.
There are three answers. The short answer is: we don't know. The slightly-longer answer is: we can speculate about how much cases could be worth by comparing them to similar medical device claims in the past, but that's just speculation. But the most important answer is: it would be unethical for us to give you any sort of guarantee, so we try not to cause any confusion about the value of the claims.
Not too long ago, I was talking to a potential medical implant client who asked me how much their claim could be worth. The implant in question was, like the DePuy hips, still in the "discovery" phase of the litigation, and so no trials had been held, and thus we had no idea how judges or juries would react to some of the evidence. I thus told the client the same thing I mentioned in the above paragraph: we don't know, and I don't want to speculate or accidentally mislead you.
In response, the client told me that another lawyer had said they were settling similar cases for $2 million to $5 million. I was shocked: it was a bold, outright lie to a potential client to convince them to sign up with that lawyer. Appalled as I was, I worry it may happen with some frequency.
Truth is, any lawyer who tells you that they "know" how much the DePuy hip cases are settling for - or who tells you they've already settling cases for significant sums of money - is not being forthright. Here's the main court page for the ASR lawsuits: it says the first jury trials begins in May 2013. Here's the main court page for the Pinnacle lawsuits: it says the first of the jury trials will be ready by September 2014. Bloomberg reported back in August 2012 that three ASR hip implant lawsuits settled for roughly $200,000, but it's premature to take those three cases as a guide, not least because we have few details about those cases, or why the plaintiffs accepted those amounts.
A lot of things could happen in the meantime, some good for plaintiffs, some bad. Here, for example, is a court opinion from the main DePuy federal judge last week, in which plaintiffs won on a procedural issue involving one of the hip implant distributors. That helps plaintiffs, but it's certainly not the whole story.
As I've said many times before, large corporate defendants - like DePuy and Johnson & Johnson - simply don't offer substantial settlements until they're right on the courthouse steps. In mass torts cases, they often don't put any real money on the table until after a couple jury trials have taken place. To put it simply, we're not going to know how much the hip implant cases are really worth until at least the Spring of 2013.
For more than fifty years, The Beasley Firm has fought for the rights of patients and consumers, obtaining over $2 billion in settlements and jury verdicts for our clients. Our DePuy recall lawyers are currently filing claims on behalf of ASR and Pinnacle hip implant patients who developed complications and were told by their doctors to have a revision or replacement surgery.
For a free and confidential consultation with our lawyers, doctors, and nurses, use the form below, call The Beasley Firm's main line at (215) 592-1000, or call my office directly at (215) 931-2634.