Nonparametric regression estimation for quasi-associated Hilbertian processes

TL;DR

This paper proves the asymptotic normality of a kernel-based regression estimator for quasi-associated data in a Hilbert space, advancing nonparametric regression theory for complex dependent data.

Contribution

It introduces a new asymptotic normality result for kernel regression estimators applied to quasi-associated Hilbertian processes, a class of dependent data.

Findings

Asymptotic normality of the estimator is established.

The results extend nonparametric regression theory to quasi-associated Hilbertian data.

The methodology applies to high-dimensional and functional data.

Abstract

We establish the asymptotic normality of the kernel type estimator for the regression function constructed from quasi-associated data when the explanatory variable takes its values in a separable Hilbert space.