A method for variable selection in a multivariate functional linear regression model

TL;DR

This paper introduces a novel variable selection method for multivariate functional linear regression models, utilizing basis expansions and penalization techniques to improve selection accuracy, validated through simulation studies.

Contribution

The paper presents a new variable selection procedure specifically designed for multivariate functional linear models, combining basis expansions with penalization for effective selection.

Findings

Effective variable selection demonstrated in simulations.

Comparison shows improved performance over existing methods.

Method suitable for models with multiple scalar responses and functional predictors.

Abstract

We propose a new variable selection procedure for a functional linear model with multiple scalar responses and multiple functional predictors. This method is based on basis expansions of the involved functional predictors and coefficients that lead to a multivariate linear regression model. Then a criterion by means of which the variable selection problem reduces to that of estimating a suitable set is introduced. Estimation of this set is achieved by using appropriate penalizations of estimates of this criterion, so leading to our proposal. A simulation study that permits to investigate the effectiveness of the proposed approach and to compare it with existing methods is given.