New Entropy Estimator with an Application to Test of Normality

TL;DR

This paper introduces a novel entropy estimator using smooth quantile density estimators, leading to a new normality test with demonstrated consistency, asymptotic properties, and comparative simulation results.

Contribution

It presents a new entropy estimator based on smooth quantile density estimators and develops a novel normality test with theoretical and simulation validation.

Findings

The estimator is consistent and asymptotically normal.

The new normality test performs well in power comparisons.

Simulation studies show improved mean squared error over existing methods.

Abstract

In the present paper we propose a new estimator of entropy based on smooth estimators of quantile density. The consistency and asymptotic distribution of the proposed estimates are obtained. As a consequence, a new test of normality is proposed. A small power comparison is provided. A simulation study for the comparison, in terms of mean squared error, of all estimators under study is performed.