Variable Selection in Semiparametric Bi-functional Models

Abstract

A new sparse semiparametric functional model is proposed, which tries to incorporate the influence of two functional variables in a scalar response in a flexible way, but involving interpretable parameters. One of the functional variables is included trough a single-index structure and the other one linearly, but trough the high-dimensional vector formed by its discretized observations. For this model, a new algorithm for variable selection in the linear part is proposed. This procedure takes advantage of the functional origin of the scalar covariates with linear effect. Some asymptotic results will ensure the good performance of the method. Finally, Tecator’s data will illustrate the great applicability of the presented methodology: good predictive power together with interpretability of the outputs.