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

DOI

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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TY  - JOUR
AU  - Amadou Diadié Ba
AU  - Gane Samb LO
AU  - Diam Ba
PY  - 2018
DA  - 2018/03/31
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  - 10.2991/jsta.2018.17.1.12
ID  - DiadiéBa2018
ER  -