Comptes Rendus
no. 10
Statistics/Probability Theory
Dual representation of φ-divergences and applications
[Représentation duale des φ-divergences et applications]

Présenté par : Paul Deheuvels

Amor Keziou1
1 LSTA, boı̂te courrier 158, 8A, Université Paris-6, 175, rue du Chevaleret, 75013 Paris, France
Comptes Rendus. Mathématique, Volume 336 (2003) no. 10, pp. 857-862.

Dans cette Note, nous donnons une représentation « duale » des divergences. Nous utilisons cette représentation pour définir et étudier de nouveaux estimateurs de la loi et des divergences pour des modèles paramétriques discrets et continus.

In this Note, we give a “dual” representation of divergences. We make use of this representation to define and study some new estimates of the law and of the divergences for discrete and continuous parametric models.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00215-2
Amor Keziou 1

1 LSTA, boı̂te courrier 158, 8A, Université Paris-6, 175, rue du Chevaleret, 75013 Paris, France 
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Amor Keziou. Dual representation of φ-divergences and applications. Comptes Rendus. Mathématique, Volume 336 (2003) no. 10, pp. 857-862. doi : 10.1016/S1631-073X(03)00215-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00215-2/

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[3] I. Csiszar On topological properties of f-divergences, Studia Sci. Math. Hungar., Volume 2 (1967), pp. 329-339

[4] A. Dembo; O. Zeitouni Large Deviations Techniques and Applications, Jones & Bartlett, 1998

[5] F. Liese; I. Vajda Convex Statistical Distances, Teubner, Leipzig, 1987

[6] B.G. Lindsay Efficiency versus robustness: the case for minimum Hellinger distance and related methods, Ann. Statist., Volume 22 (1994), pp. 1081-1114

[7] D. Morales; L. Pardo; I. Vajda Asymptotic divergence of estimates of discrete distributions, J. Statist. Plann. Inference, Volume 48 (1995) no. 3, pp. 347-369

[8] L. Rüschendorf On the minimum discrimination information theorem, Statist. Decisions, Suppl., Volume 1 (1984), pp. 263-283

[9] A. van der Vaart Asymptotic Statistics, Cambridge Series in Statistical and Probabilitic Mathematics, 1998

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