# Divergence measures estimation and its asymptotic normality theory in the discrete case

## TL;DR

This paper develops the asymptotic theory for $\

## Contribution

It introduces the asymptotic properties of $\

## Key findings

- Asymptotic normality of divergence estimators established.
- Validation of theoretical results through simulations.
- Derivation of statistical tests based on divergence measures.

## Abstract

In this paper we provide the asymptotic theory of the general of $\phi$-divergences measures, which include the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. We are interested in divergence measures in the discrete case. One sided and two-sided statistical tests are derived as well as symmetrized estimators. Almost sure rates of convergence and asymptotic normality theorem are obtained in the general case, and next particularized for the Renyi and Tsallis families and for the Kullback-Leibler measure as well. Our theorical results are validated by simulations.