Central limit theorem for the variable bandwidth kernel density estimators

TL;DR

This paper investigates the asymptotic distribution of variable bandwidth kernel density estimators, establishing central limit theorems for both ideal and practical versions based on bias and variance analysis.

Contribution

It provides the first comprehensive central limit theorem results for the variable bandwidth kernel density estimators, including the practical plug-in version.

Findings

Central limit theorem established for ideal variable bandwidth estimators

Central limit theorem established for practical plug-in estimators

Bias and variance analysis underpinning the CLT results

Abstract

In this paper we study the ideal variable bandwidth kernel density estimator introduced by McKay (1993) and Jones, McKay and Hu (1994) and the plug-in practical version of the variable bandwidth kernel estimator with two sequences of bandwidths as in Gin\'e and Sang (2013). Based on the bias and variance analysis of the ideal and true variable bandwidth kernel density estimators, we study the central limit theorems for each of them.