Nonlinear Multivariate Function-on-function Regression with Variable Selection

Fuente: arXiv
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Main Authors: Haijie, Xu, Chen, Zhang
Format: Preprint
Published: 2024
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author Haijie, Xu
Chen, Zhang
author_facet Haijie, Xu
Chen, Zhang
contents This paper proposes a multivariate nonlinear function-on-function regression model, which allows both the response and the covariates can be multi-dimensional functions. The model is built upon the multivariate functional reproducing kernel Hilbert space (RKHS) theory. It predicts the response function by linearly combining each covariate function in their respective functional RKHS, and extends the representation theorem to accommodate model estimation. Further variable selection is proposed by adding the lasso penalty to the coefficients of the kernel functions. A block coordinate descent algorithm is proposed for model estimation, and several theoretical properties are discussed. Finally, we evaluate the efficacy of our proposed model using simulation data and a real-case dataset in meteorology.
format Preprint
id arxiv_https___arxiv_org_abs_2406_19021
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Nonlinear Multivariate Function-on-function Regression with Variable Selection
Haijie, Xu
Chen, Zhang
Methodology
This paper proposes a multivariate nonlinear function-on-function regression model, which allows both the response and the covariates can be multi-dimensional functions. The model is built upon the multivariate functional reproducing kernel Hilbert space (RKHS) theory. It predicts the response function by linearly combining each covariate function in their respective functional RKHS, and extends the representation theorem to accommodate model estimation. Further variable selection is proposed by adding the lasso penalty to the coefficients of the kernel functions. A block coordinate descent algorithm is proposed for model estimation, and several theoretical properties are discussed. Finally, we evaluate the efficacy of our proposed model using simulation data and a real-case dataset in meteorology.
title Nonlinear Multivariate Function-on-function Regression with Variable Selection
topic Methodology
url https://arxiv.org/abs/2406.19021