Uniform-in-bandwidth consistency for nonparametric estimation of divergence measures

TL;DR

This paper introduces a nonparametric kernel-based method for estimating divergence measures between continuous distributions, establishing uniform-in-bandwidth consistency and providing asymptotic confidence intervals.

Contribution

It presents a novel kernel-based estimator for divergence measures with proven uniform-in-bandwidth consistency and asymptotic confidence intervals.

Findings

Estimator is uniformly consistent across bandwidths.

Asymptotic 100% confidence intervals are derived.

Method improves reliability of divergence estimation.

Abstract

We propose nonparametric estimation of divergence measures between continuous distributions. Our approach is based on a plug-in kernel- type estimators of density functions. We give the uniform in bandwidth consistency for the proposal estimators. As a consequence, their asymp- totic 100% confidence intervals are also provided.