Sparse varying-coefficient functional linear model

TL;DR

This paper introduces a penalized maximum likelihood approach for variable selection in varying-coefficient functional linear models, enabling identification of relevant predictors and their effects on a scalar response, with applications to crop yield analysis.

Contribution

It proposes a novel sparse estimation method for varying-coefficient functional linear models, allowing for effective variable selection and interpretation of predictor effects.

Findings

Method successfully identifies relevant functional predictors.

Simulation studies confirm effectiveness of the approach.

Application to crop data reveals key environmental factors.

Abstract

We consider the problem of variable selection in varying-coefficient functional linear models, where multiple predictors are functions and a response is a scalar and depends on an exogenous variable. The varying-coefficient functional linear model is estimated by the penalized maximum likelihood method with the sparsity-inducing penalty. Tuning parameters that controls the degree of the penalization are determined by a model selection criterion. The proposed method can reveal which combination of functional predictors relates to the response, and furthermore how each predictor relates to the response by investigating coefficient surfaces. Simulation studies are provided to investigate the effectiveness of the proposed method. We also apply it to the analysis of crop yield data to investigate which combination of environmental factors relates to the amount of a crop yield.