Partially functional linear regression in reproducing kernel Hilbert spaces

Abstract

In this paper, we study the partially functional linear regression model in which there are both functional predictors and traditional multivariate predictors. The existing approach is based on approximation using functional principal component analysis which has some limitations. We propose an alternative framework based on reproducing kernel Hilbert spaces (RKHS) which has not been investigated in the literature for the partially functional case. Asymptotic normality of the non-functional part is also shown. Even when reduced to the purely functional linear regression, our results extend the existing results in two aspects: rates are established using both prediction risk and RKHS norm, and faster rates are possible if greater smoothness is assumed. Some simulations are used to demonstrate the performance of the proposed estimator.