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.

40 pages, 7 figures, 5 tables

References in corpus (5)

• Estimation and testing for partially linear single-index models
• SCAD-penalized regression in high-dimensional partially linear models
• Single and multiple index functional regression models with nonparametric link
• Methodology and theory for partial least squares applied to functional data
• Automatic and location-adaptive estimation in functional single-index regression

Cited by in corpus (2)

• Variable selection in functional regression models: a review
• Fast and efficient algorithms for sparse semiparametric bi-functional regression