Journal of Statistical Theory and Applications

Volume 17, Issue 1, March 2018, Pages 158 - 171

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

Authors
Amadou Diadié Baamadou-diadie.ba@edu.ugb.en
LERSTAD, Gaston Berger University, Saint-Louis, SENEGAL
Gane Samb LOgane-samb.lo@ugb.edu.sn gslo@aust.edu.ng
LERSTAD, Gaston Berger University, Saint-Louis, SENEGAL *, Associate Researcher, LASTA, Pierre et Marie University, Paris, FRANCE, Assiated Professor, African University of Sciences and Technology, Abuja, NIGERIA
Diam Badiam.ba@edu.ugb.en
LERSTAD, Gaston Berger University, Saint-Louis, SENEGAL
*

1178, Evanston Drive, NW, Calgary, Canada, T3P 0J9

Received 8 May 2017, Accepted 21 December 2017, Available Online 31 March 2018.
DOI
https://doi.org/10.2991/jsta.2018.17.1.12How to use a DOI?
Keywords
Divergence measures estimation, Asymptotic normality, Wavelet theory, wavelets empirical processes, Besov spaces
Abstract

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.

Copyright
Copyright © 2018, the Authors. Published by Atlantis Press.
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

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Journal
Journal of Statistical Theory and Applications
Volume-Issue
17 - 1
Pages
158 - 171
Publication Date
2018/03
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.2018.17.1.12How to use a DOI?
Copyright
Copyright © 2018, the Authors. Published by Atlantis Press.
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Amadou Diadié Ba
AU  - Gane Samb LO
AU  - Diam Ba
PY  - 2018
DA  - 2018/03
TI  - Divergence Measures Estimation and Its Asymptotic Normality Theory Using Wavelets Empirical Processes I
JO  - Journal of Statistical Theory and Applications
SP  - 158
EP  - 171
VL  - 17
IS  - 1
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2018.17.1.12
DO  - https://doi.org/10.2991/jsta.2018.17.1.12
ID  - DiadiéBa2018
ER  -