Sparse semiparametric regression when predictors are mixture of functional and high-dimensional variables

Abstract

This paper aims to front with dimensionality reduction in regression setting when the predictors are a mixture of functional variable and high-dimensional vector. A flexible model, combining both sparse linear ideas together with semiparametrics, is proposed. A wide scope of asymptotic results is provided: this covers as well rates of convergence of the estimators as asymptotic behaviour of the variable selection procedure. Practical issues are analysed through finite sample-simulated experiments, while an application to Tecator’s data illustrates the usefulness of our methodology.