Consistency of the recursive nonparametric regression estimation for dependent functional data

TL;DR

This paper proves the almost sure convergence and analyzes the mean quadratic error of recursive nonparametric regression estimators for dependent functional data, under strong mixing conditions, providing theoretical guarantees for their performance.

Contribution

It introduces new convergence results and error bounds for recursive regression estimators in the context of dependent functional data, extending existing theory.

Findings

Almost sure convergence of estimators established

Derived mean quadratic error with rates and bounds

Results applicable under strong mixing dependence

Abstract

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the mean quadratic error of the considered class of estimators. Our results are established with rates and asymptotic appear bounds, under strong mixing condition.