Conditional Shannon, R\'eyni, and Tsallis entropies estimation and asymptotic limits: discrete case

A method of estimating the joint probability mass function of a pair of discrete random variables is described. This estimator is used to construct the conditional Shannon-R'eyni-Tsallis entropies estimates. From there almost sure rates of convergence and asymptotic normality are established. The theorical results are validated by simulations.