Variable selection in Functional Additive Regression Models

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.