Multiple functional regression with both discrete and continuous covariates

TL;DR

This paper introduces a nonparametric approach for multiple functional regression that accommodates both discrete and continuous covariates using reproducing kernel Hilbert spaces and positive operator-valued kernels.

Contribution

It extends functional regression to handle multiple covariates of mixed types with a novel kernel-based nonparametric method.

Findings

Supports mixed discrete and continuous variables

Uses positive operator-valued kernels for estimation

Provides a flexible nonparametric framework

Abstract

In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al. (2010a), the method, which support mixed discrete and continuous explanatory variables, is based on estimating a function-valued function in reproducing kernel Hilbert spaces by virtue of positive operator-valued kernels.