Recursive estimation of nonparametric regression with functional covariate

TL;DR

This paper develops a recursive kernel method for estimating regression functions with functional covariates, providing convergence rates, a CLT, and empirical validation.

Contribution

It introduces a recursive nonparametric kernel estimator for functional data, with theoretical convergence results and practical evaluation.

Findings

Mean square error bounds established

Almost sure convergence proved

Central limit theorem derived

Abstract

The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of recursive kernel estimates of the regression function are derived. These results are established with rates and precise evaluation of the constant terms. Also, a central limit theorem for this class of estimators is established. The method is evaluated on simulations and real data set studies.