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

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 Rényi-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.

20 pages, 4 figures