Abstract: Variable selection is considered in the setting of supervised binary classification with functional data {X(t), t ∈ [0,1]}. By “variable selection” we mean any dimension-reduction method that leads to the replacement of the whole trajectory {X(t), t ∈ [0,1]}, with a low-dimensional vector (X(t₁),…,X(t_d)) still keeping a similar classification error. Our proposal for variable selection is based on the idea of selecting the local maxima (t₁,…,t_d) of the function _X²(t) = ²(X(t),Y ), where denotes the “distance covariance” association measure for random variables due to Székely, Rizzo, and Bakirov (2007). This method provides a simple natural way to deal with the relevance vs. redundancy trade-off which typically appears in variable selection. A result of consistent estimation for the maxima of _X² is shown. We also show different models for the underlying process X(t) under which the relevant information is concentrated on the maxima of _X². An extensive empirical study is presented, including about 400 simulated models and data examples aimed at comparing our variable selection method with other standard proposals for dimension reduction.

Key words and phrases: Distance correlation, functional data analysis, supervised classification, variable selection.