Divergence Measures Estimation and Its Asymptotic Normality Theory Using Wavelets Empirical Processes I

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 famili...

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Bibliographic Details
Published in:Journal of statistical theory and applications Vol. 17; no. 1; pp. 158 - 171
Main Authors: Ba, Amadou Diadié, LO, Gane Samb, Ba, Diam
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.03.2018
Springer Nature B.V
Springer
Subjects:
Asymptotic methods
Asymptotic normality
Asymptotic properties
Besov spaces
Divergence
Divergence measures estimation
Estimators
Function space
Normality
Probability density functions
Research Article
Statistical analysis
Statistical tests
Wavelet theory
wavelets empirical processes
62G05
62G07
Divergence measures estimation
Asymptotic normality
62G20
Wavelet theory
Besov spaces
wavelets empirical processes
ISSN:1538-7887, 2214-1766, 1538-7887
Online Access:Get full text
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Summary: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.
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ISSN:1538-7887
2214-1766
1538-7887
DOI:10.2991/jsta.2018.17.1.12