Variable Selection in Multivariate Functional Linear Regression

Chi-Kuang Yeh and Peijun Sang ()
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Chi-Kuang Yeh: University of Waterloo
Peijun Sang: University of Waterloo

Statistics in Biosciences, 2025, vol. 17, issue 1, No 3, 17-34

Abstract: Abstract Multivariate functional linear regression is commonly adopted to model the effects of several function-valued covariates on a scalar response. To select functional covariates with a time-varying effect, we develop a framework based on the reproducing kernel Hilbert space (RKHS). In particular, each coefficient function is assumed to reside in this RKHS and an RKHS norm is chosen as the penalty function in the regularized empirical risk function. This special penalty term enables us to achieve sparsity and smoothness when fitting multivariate functional linear models. Moreover, simulation studies demonstrate that the proposed estimator compares favorably with some traditional methods in variable selection, function estimation and prediction in finite samples. Finally, we apply the proposed framework to two real examples.

Keywords: Reproducing kernel Hilbert space; Method of regularization; Functional data analysis; Functional linear regression (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s12561-023-09373-x

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