Strongly Consistent of Kullback-Leibler Divergence Estimator and Tests for Model Selection Based on a Bias Reduced Kernel Density Estimator

TL;DR

This paper introduces a bias-reduced kernel density estimator with strong consistency for Kullback-Leibler divergence, enabling reliable goodness-of-fit and model selection tests validated through simulations.

Contribution

It develops a strongly consistent KLD estimator based on a bias-reduced kernel density estimator, along with new goodness-of-fit and model selection tests.

Findings

The proposed estimator is strongly consistent.

The tests perform well in Monte Carlo simulations.

The methods are effective for model selection.

Abstract

In this paper, we study the strong consistency of a bias reduced kernel density estimator and derive a strongly con- sistent Kullback-Leibler divergence (KLD) estimator. As application, we formulate a goodness-of-fit test and an asymptotically standard normal test for model selection. The Monte Carlo simulation show the effectiveness of the proposed estimation methods and statistical tests.