Variable bandwidth kernel regression estimation

TL;DR

This paper introduces a variable bandwidth kernel regression estimator in  dimensions that improves bias and provides central limit theorems, with simulations confirming its advantages over classical methods.

Contribution

It proposes a novel variable bandwidth kernel estimator with higher-order bias reduction and establishes its asymptotic normality, enhancing regression estimation accuracy.

Findings

Bias reduced to order O(h_n^4)

Central limit theorems established for the estimator

Simulation confirms improved performance over classical kernel methods

Abstract

In this paper we propose a variable bandwidth kernel regression estimator for $i.i.d.$ observations in $\mathbb{R}^2$ to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of $O(h_n^4)$ under the condition that the fifth order derivative of the density function and the sixth order derivative of the regression function are bounded and continuous. We also establish the central limit theorems for the proposed ideal and true variable kernel regression estimators. The simulation study confirms our results and demonstrates the advantage of the variable bandwidth kernel method over the classical kernel method.