Divergence Measures Estimation and its Asymptotic Normality Theory in the Discrete Case

In this paper we provide the asymptotic theory of the general of φ-divergences measures, which include the most common divergence measures : R´enyi and Tsallis families and the Kullback-Leibler measure. We are interested in divergence measures in the discrete case. One sided and two-sided statisti...

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Bibliographic Details
Published in:European journal of pure and applied mathematics 2019-01, Vol.12 (3), p.790-820
Main Authors: Ba, Amadou Diadie, Lo, Gane Samb
Format: Article
Language:English
Online Access:Get full text
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Summary:In this paper we provide the asymptotic theory of the general of φ-divergences measures, which include the most common divergence measures : R´enyi 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 R´enyi and Tsallis families and for the Kullback-Leibler measure as well. Our theoretical results are validated by simulations.
ISSN:1307-5543
1307-5543
DOI:10.29020/nybg.ejpam.v12i3.3437