  The random coefficients model $Y_i={\beta_0}_i+{\beta_1}_i
{X_1}_i+{\beta_2}_i {X_2}_i+\ldots+{\beta_d}_i {X_d}_i$, with $\mathbf{X}_i$,
$Y_i$, $\mathbf{\beta}_i$ i.i.d, and $\mathbf{\beta}_i$ independent of $X_i$ is
often used to capture unobserved heterogeneity in a population. We propose a
quasi-maximum likelihood method to estimate the joint density distribution of
the random coefficient model. This method implicitly involves the inversion of
the Radon transformation in order to reconstruct the joint distribution, and
hence is an inverse problem. Nonparametric estimation for the joint density of
$\mathbf{\beta}_i=({\beta_0}_i,\ldots, {\beta_d}_i)$ based on kernel methods or
Fourier inversion have been proposed in recent years. Most of these methods
assume a heavy tailed design density $f_\mathbf{X}$. To add stability to the
solution, we apply regularization methods. We analyze the convergence of the
method without assuming heavy tails for $f_\mathbf{X}$ and illustrate
performance by applying the method on simulated and real data. To add stability
to the solution, we apply a Tikhonov-type regularization method.

Methodology;Applications