Consistent Variable Selection for Functional Regression Models

TL;DR

This paper introduces a new variable selection method for functional linear regression models that uses basis expansions and likelihood ratio tests, demonstrating superior performance through simulations and real data analysis.

Contribution

It proposes a consistent variable selection procedure for functional regression models that handles growing predictor sets and outperforms existing methods.

Findings

The method is consistent in selecting relevant predictors.

Simulations show improved accuracy over existing methods.

Application to weather data illustrates practical utility.

Abstract

The dual problem of testing the predictive significance of a particular covariate, and identification of the set of relevant covariates is common in applied research and methodological investigations. To study this problem in the context of functional linear regression models with predictor variables observed over a grid and a scalar response, we consider basis expansions of the functional covariates and apply the likelihood ratio test. Based on p-values from testing each predictor, we propose a new variable selection method, which is consistent in selecting the relevant predictors from set of available predictors that is allowed to grow with the sample size n. Numerical simulations suggest that the proposed variable selection procedure outperforms existing methods found in the literature. A real dataset from weather stations in Japan is analyzed.