Nonlinear Multivariate Function-on-function Regression with Variable Selection

TL;DR

This paper introduces a nonlinear multivariate function-on-function regression model utilizing RKHS theory, incorporating variable selection via lasso penalty, and demonstrates its effectiveness through simulations and meteorological data.

Contribution

It develops a novel multivariate nonlinear function-on-function regression framework with integrated variable selection based on RKHS and lasso penalty.

Findings

Effective variable selection with lasso penalty.

Strong performance demonstrated on simulation data.

Successful application to meteorological dataset.

Abstract

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.