Divergence Measures Estimation and Its Asymptotic Normality Theory Using Wavelets Empirical Processes III

In the two previous papers of this series, the main results on the asymptotic behaviors of empirical divergence measures based on wavelets theory have been established and particularized for important families of divergence measures like Rényi and Tsallis families and for the Kullback-Leibler measures. While the proofs of the results in the second paper may be skipped, the proofs of those in paper 1 are to be thoroughly proved since they serve as a foundation to the whole structure of results. We prove them in this last paper of the series. We will also address the applicability of the results to usual distribution functions.