Kernel-Type Estimators of Divergence Measures and Its Strong Uniform Consistency
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 1, January 2016, Pages: 13-22
Received: Jan. 8, 2016; Accepted: Jan. 23, 2016; Published: Feb. 16, 2016
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Hamza Dhaker, Departement de Mathématiques et Informatique, Faculté des Sciences et Technique, Université Cheikh Anta Diop, Dakar, Sénégal
Papa Ngom, Departement de Mathématiques et Informatique, Faculté des Sciences et Technique, Université Cheikh Anta Diop, Dakar, Sénégal
El Hadji Deme, Sciences Appliquées et Technologie, Unité de Formation et de Recherche, Université Gaston Berger, Saint-Louis, Sénégal
Pierre Mendy, Département de Techniques Quantitatives, Faculté des Sciences Economiques et de Gestion, Université Cheikh Anta Diop , Dakar, Sénégal
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Nonparametric density estimation, based on kernel-type estimators, is a very popular method in statistical research, especially when we want to model the probabilistic or stochastic structure of a data set. In this paper, we investigate the asymptotic confidence bands for the distribution with kernel-estimators for some types of divergence measures (Rényi-α and Tsallis-α divergence). Our aim is to use the method based on empirical process techniques, in order to derive some asymptotic results. Under different assumptions, we establish a variety of fundamental and theoretical properties, such as the strong consistency of an uniform-in-bandwidth of the divergence estimators. We further apply the previous results in simulated examples, including the kernel-type estimator for Hellinger, Bhattacharyya and Kullback-Leibler divergence, to illustrate this approach, and we show that that the method performs competitively.
Divergence Measures, Kernel Estimation, Strong Uniform, Consistency
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Hamza Dhaker, Papa Ngom, El Hadji Deme, Pierre Mendy, Kernel-Type Estimators of Divergence Measures and Its Strong Uniform Consistency, American Journal of Theoretical and Applied Statistics. Vol. 5, No. 1, 2016, pp. 13-22. doi: 10.11648/j.ajtas.20160501.13
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