文章基本信息

标题：Divergence Measures Estimation and Its Asymptotic Normality Theory Using Wavelets Empirical Processes I
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作者：Amadou Diadié Ba ; Gane Samb LO ; Diam Ba 等
期刊名称：Journal of Statistical Theory and Applications (JSTA)
电子版ISSN：1538-7887
出版年度：2018
卷号：17
期号：1
页码：160-173
DOI：10.2991/jsta.2018.17.1.12
语种：English
出版社：Atlantis Press
摘要：We deal with the normality asymptotic theory of empirical divergences measures based on wavelets in a series of three papers. In this first paper, we provide the asymptotic theory of the general of ϕ-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measures. Instead of using the Parzen nonparametric estimators of the probability density functions whose discrepancy is estimated, we use the wavelets approach and the geometry of Besov spaces. One-sided and two-sided statistical tests are derived. This paper is devoted to the foundations the general asymptotic theory and the exposition of the mains theoretical tools concerning the ϕ-forms, while proofs and next detailed and applied results will be given in the two subsequent papers which deal important key divergence measures and symmetrized estimators.
关键词：Divergence measures estimation;Asymptotic normality;Wavelet theory;wavelets empirical processes;Besov spaces