# Non parametric estimation of joint, Renyi-Stallis entropies and mutual information and asymptotic limits

## TL;DR

This paper introduces a new non-parametric method for estimating joint entropies and mutual information of discrete variables, with proven consistency and asymptotic properties validated through simulations.

## Contribution

It presents a novel estimator for joint probability mass functions and entropy measures, along with theoretical guarantees and empirical validation.

## Key findings

- Estimator is almost surely consistent
- Central limit theorems are established for the estimators
- Simulation results validate the theoretical properties

## Abstract

This paper proposes a new method for estimating the joint probability mass function of a pair of discrete random variables. This estimator is used to construct joint Shannon R\'enyi-Tsallis entropies, and the mutual information estimates of a pair of discrete random variables. Almost sure consistency and central limit Theorems are established. Our theorical results are validated by simulations.