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Variable Selection in Multivariate Functional Linear Regression

Author

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  • Chi-Kuang Yeh

    (University of Waterloo)

  • Peijun Sang

    (University of Waterloo)

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.

Suggested Citation

  • Chi-Kuang Yeh & Peijun Sang, 2025. "Variable Selection in Multivariate Functional Linear Regression," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 17(1), pages 17-34, April.
    • Handle: RePEc:spr:stabio:v:17:y:2025:i:1:d:10.1007_s12561-023-09373-x
    DOI: 10.1007/s12561-023-09373-x
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    References listed on IDEAS

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