The functional regression model with scalar response (FRM) is stated as follows: Let X,y two random variates taking values in E×R where E is a functional space (semi-metric, normed or Hilbert). The relationship between the two variates can be expressed as follows: y=m(X)+ϵ=E(y|X)+ϵ(1) where ϵ is a real random variable verifying E(ϵ|X)=0. Depending on the nature of the functional space E and on the regression operator m, we can classify the different types of FRM: Multivariate Linear Model: E=Rp and m is the linear operator in the space, i.e. E(y|X)=Xβ with β∈Rp.Functional Linear Model: E=L2(T) is the Hilbert space of square integrable functions over T = [a, b] and m is a linear operator in the space, i.e. m(X)=〈X,β〉 with β∈L2(T). This model has been treated extensively in the literature mainly devoted to the optimal way of representing the linear operator through the representation of X and β on a basis of L2(T).Depending on the latter, the references can be classified into two main categories: Fixed basis. The most commonly used basis in this context are the Fourier , the B-spline  and the Wavelet .Data-driven basis. Two main basis computed from the data are used in the literature: the most parsimonious one is given by the functional principal components [19, 20] and the one that maximizes the covariance among the response and the functional predictor uses the functional partial least square components (PLS) [21, 22].Note that, due to the representation employed, the FRM is always an approximated model and its goodness typically relies on the properties of the chosen basis and its suitability to the data at hand.Functional Non Linear Model: E is (at least) a semi-metric space and m is a continuous operator i.e. limX′→Xm(X′)=m(X). For a complete review of this model see Ferraty and Vieu  and the references therein.Extensions of the above models: The above models could be extended in several ways, usually considering more than one predictive variate. This could lead to semi-linear models [23, 24], additive models [25, 26], , single index models [28, 29] or projection pursuit models .