A Bayesian Nonparametric Estimation to Entropy

TL;DR

This paper introduces a Bayesian nonparametric estimator for entropy using the Dirichlet process, combining classical estimators with Bayesian methods, and demonstrates its consistency and superior performance through theoretical analysis and examples.

Contribution

It presents a novel Bayesian nonparametric entropy estimator based on the Dirichlet process, extending classical estimators with theoretical guarantees.

Findings

The estimator is consistent.

It exhibits excellent performance in examples.

Theoretical properties are established.

Abstract

A Bayesian nonparametric estimator to entropy is proposed. The derivation of the new estimator relies on using the Dirichlet process and adapting the well-known frequentist estimators of Vasicek (1976) and Ebrahimi, Pflughoeft and Soofi (1994). Several theoretical properties, such as consistency, of the proposed estimator are obtained. The quality of the proposed estimator has been investigated through several examples, in which it exhibits excellent performance.