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

Authors

  • Amadou Diadie Ba Gaston Berger University, Sénégal
  • Gane Samb Lo

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i3.3437

Keywords:

Phi-divergence measure estimation

Abstract

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.

Author Biography

  • Amadou Diadie Ba, Gaston Berger University, Sénégal
    Statistics and Probability laboratory

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Published

2019-07-25

Issue

Vol. 12 No. 3: (July 2019)

Section

Nonlinear Analysis

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How to Cite

Divergence Measures Estimation and its Asymptotic Normality Theory in the Discrete Case. (2019). European Journal of Pure and Applied Mathematics, 12(3), 790-820. https://doi.org/10.29020/nybg.ejpam.v12i3.3437