Variable selection in Functional Additive Regression Models

TL;DR

This paper introduces a sequential variable selection method for functional additive regression models using distance correlation, capable of handling mixed variable types and assessing their contribution, with promising simulation and real data results.

Contribution

It proposes a novel variable selection algorithm for functional additive models that can evaluate different types of variable contributions, including non-linear effects.

Findings

Effective variable selection demonstrated in simulations

Successful application to real datasets

Algorithm assesses linear and non-linear contributions

Abstract

This paper considers the problem of variable selection in regression models in the case of functional variables that may be mixed with other type of variables (scalar, multivariate, directional, etc.). Our proposal begins with a simple null model and sequentially selects a new variable to be incorporated into the model based on the use of distance correlation proposed by \cite{Szekely2007}. For the sake of simplicity, this paper only uses additive models. However, the proposed algorithm may assess the type of contribution (linear, non linear, ...) of each variable. The algorithm has shown quite promising results when applied to simulations and real data sets.