Sparsity learning via structured functional factor augmentation

TL;DR

This paper introduces a novel structured functional factor augmentation method for high-dimensional multivariate functional regression, addressing correlation challenges among covariates with theoretical backing and demonstrating superior estimation and selection performance.

Contribution

It proposes the fFAS and fFASM models, providing the first structured approach to handle correlated functional covariates in high-dimensional settings with theoretical and empirical validation.

Findings

fFASM achieves high estimation accuracy.

fFASM demonstrates consistent variable selection.

Theoretical properties are rigorously established.

Abstract

As one of the most powerful tools for examining the association between functional covariates and a response, the functional regression model has been widely adopted in various interdisciplinary studies. Usually, a limited number of functional covariates are assumed in a functional linear regression model. Nevertheless, correlations may exist between functional covariates in high-dimensional functional linear regression models, which brings significant statistical challenges to statistical inference and functional variable selection. In this article, a novel functional factor augmentation structure (fFAS) is proposed for multivariate functional series, and a multivariate functional factor augmentation selection model (fFASM) is further proposed to deal with issues arising from variable selection of correlated functional covariates. Theoretical justifications for the proposed fFAS are provided, and statistical inference results of the proposed fFASM are established. Numerical investigations support the superb performance of the novel fFASM model in terms of estimation accuracy and selection consistency.