Divergence Measures Estimation and Its Asymptotic Normality Theory Using Wavelets Empirical Processes I
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- https://doi.org/10.2991/jsta.2018.17.1.12How to use a DOI?
- Divergence measures estimation, Asymptotic normality, Wavelet theory, wavelets empirical processes, Besov spaces
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 © 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 -