Divergence measures estimation and its asymptotic normality theory using wavelets empirical processes II

Abstract

In Ba et al.(2017), a general normal asymptotic theory for divergence measures estimators has been provided. These estimators are constructed from the wavelets empirical process and concerned the general Ø-divergence measures. In this paper, we first extend the aforementioned results to symmetrized forms of divergence measures. Second, the Tsallis and Renyi divergence measures as well as the Kullback-Leibler measures are investigated in details. The question of the applicability of the results, based on the boundedness assumption is also dealt, leading to future packages.

Keywords: Divergence measures estimation; Asymptotic normality; Wavelet theory; wavelets empirical processes; Besov spaces

AMS 2010 Mathematics Subject Classification : 62G05; 62G20; 62G07