Variable bandwidth kernel regression estimation

¹ Department of Mathematics, University of Central Arkansas, Conway, AR 72035, USA.
² Department of Mathematics, The University of Mississippi, University, MS 38677, USA.
³ Division of Arts and Sciences, Mississippi State University at Meridian, Meridian, MS 39307, USA.

^* Corresponding author: sang@olemiss.edu

Received: 10 January 2020
Accepted: 12 January 2021

Abstract

In this paper we propose a variable bandwidth kernel regression estimator for i.i.d. observations in ℝ² to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of O(h_n⁴) 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.