Selection Model in Functional Linear Regression Models for Scalar Response

The so-called Functional Linear Regression model consists in explaining a scalar response by a regressor which is a random function observed on a compact subset of R: in this context, the “parameter” of linear model is a function of the weights. In order to estimate this functional coefficient some estimators such as Functional Principal Component Regression Estimator, Smooth Principal Component Regression Estimator, Penalized B-Splines Estimator, have been introduced in literature. We focus our attention on the Functional Principal Component Regression Estimator and in particular on the connected dimensionality problem. Our aim is to apply and compare some different selection methods, which have been proposed in the classical regression field. These methods are illustrated and compared by the means of simulations.