Asymptotic normality of recursive estimators under strong mixing conditions

TL;DR

This paper establishes the asymptotic normality of recursive nonparametric kernel estimators for regression functions under strong mixing conditions, extending previous work on Devroye-Wagner estimates.

Contribution

It provides a general asymptotic normality result for recursive kernel estimators under strong mixing, broadening the theoretical understanding of their statistical properties.

Findings

Asymptotic normality proven for recursive kernel estimators

Extension of Devroye-Wagner estimate analysis

Applicable under strong mixing conditions

Abstract

The main purpose of this paper is to estimate the regression function by using a recursive nonparametric kernel approach. We derive the asymptotic normality for a general class of recursive kernel estimate of the regression function, under strong mixing conditions. Our purpose is to extend the work of Roussas and Tran [17] concerning the Devroye-Wagner estimate.