Afrika Statistika

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

Amadou Diadié Ba, Gane Samb Lo, and Diam Ba

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Abstract

In Ba et al. (2017), a general normal asymptotic theory for divergence measures estimators has been provided. These estimators are constructed from the wavelets empirical process and concerned the general $\phi$-divergence measures. In this paper, we first extend the aforementioned results to symmetrized forms of divergence measures. Second, the Tsallis and Renyi divergence measures as well as the Kullback-Leibler measures are investigated in details. The question of the applicability of the results, based on the boundedness assumption is also dealt, leading to future packages.

Résumé

Dans Ba et al. (2017), une théorie asymptotique normale générale pour les estimateurs de mesures de divergence a été fournie. Ces estimateurs sont construits à partir du processus empirique basé sur les des ondelettes et concernait les mesures générales de divergence phi. Dans cet article, nous étendons d'abord les résultats susmentionnés à des formes symétrisées de mesures de divergence. Deuxièmement, les mesures de divergence Tsallis et Renyi ainsi que les mesures de Kullback-Leibler sont étudiées en détail. La question de l'applicabilité des résultats, basée sur l'hypothèse de densités bornées, est également abordée, conduisant à de futurs programmes informatiques.

Article information

Source
Afr. Stat., Volume 13, Number 2 (2018), 1667-1681.

Dates
First available in Project Euclid: 7 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.as/1528336826

Digital Object Identifier
doi:10.16929/as/1667.127

Mathematical Reviews number (MathSciNet)
MR3811763

Zentralblatt MATH identifier
06885666

Subjects
Primary: 62G05: Estimation 62G20: Asymptotic properties 62G07: Density estimation

Keywords
Divergence measures estimation Asymptotic normality Wavelet theory wavelets empirical processes Besov spaces

Citation

Ba, Amadou Diadié; Lo, Gane Samb; Ba, Diam. Divergence Measures Estimation and Its Asymptotic Normality Theory Using Wavelets Empirical Processes II. Afr. Stat. 13 (2018), no. 2, 1667--1681. doi:10.16929/as/1667.127. https://projecteuclid.org/euclid.as/1528336826


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