Statistics and Its Interface

Volume 17 (2024)

Number 1

Special issue in honor of Professor Lincheng Zhao

A nonparametric concurrent regression model with multivariate functional inputs

Pages: 69 – 78

DOI: https://dx.doi.org/10.4310/23-SII782

Authors

Yutong Zhai (Department of Statistics and Finance, Management School, University of Science and Technology of China, Hefei, China)

Zhanfeng Wang (Department of Statistics and Finance, Management School, University of Science and Technology of China, Hefei, China)

Yuedong Wang (Department of Statistics and Applied Probability, University of California, Santa Barbara, Calif., U.S.A.)

Abstract

Regression models with functional responses and covariates have attracted extensive research. Nevertheless, there is no existing method for the situation where the functional covariates are bivariate functions with one of the variables in common with the response function. In this article, we propose a nonparametric function-on-function regression method. We construct model spaces using a Gaussian kernel function and smoothing spline ANOVA decomposition. We estimate the nonparametric function using penalized likelihood and study properties of the Gaussian kernel function and the convergence rate of the proposed estimation method. We evaluate the proposed methods using simulations and illustrate them using two real data examples.

Keywords

function-on-function regression, Gaussian kernel, reproducing kernel Hilbert space, smoothing spline

Received 18 November 2022

Accepted 4 February 2023

Published 27 November 2023