Bandwidth Selection for Weighted Kernel Density Estimation

TL;DR

This paper introduces new bandwidth selection methods for weighted kernel density estimation, addressing boundary issues and demonstrating effectiveness through simulations and real data applications.

Contribution

It proposes three mean integrated squared error based bandwidth estimators and studies adaptive and boundary correction techniques for weighted KDE.

Findings

New bandwidth estimators outperform existing methods in simulations.

Adaptive and boundary correction methods improve density estimation accuracy.

Real data application demonstrates practical utility of the proposed methods.

Abstract

In the this paper, the authors propose to estimate the density of a targeted population with a weighted kernel density estimator (wKDE) based on a weighted sample. Bandwidth selection for wKDE is discussed. Three mean integrated squared error based bandwidth estimators are introduced and their performance is illustrated via Monte Carlo simulation. The least-squares cross-validation method and the adaptive weight kernel density estimator are also studied. The authors also consider the boundary problem for interval bounded data and apply the new method to a real data set subject to informative censoring.