Comptes Rendus
Statistics/Probability Theory
Dual representation of φ-divergences and applications
Comptes Rendus. Mathématique, Volume 336 (2003) no. 10, pp. 857-862.

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.

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.

Received:
Accepted:
Published online:
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
@article{CRMATH_2003__336_10_857_0,
     author = {Amor Keziou},
     title = {Dual representation of \protect\emph{\ensuremath{\varphi}}-divergences and applications},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {857--862},
     publisher = {Elsevier},
     volume = {336},
     number = {10},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00215-2},
     language = {en},
}
TY  - JOUR
AU  - Amor Keziou
TI  - Dual representation of φ-divergences and applications
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 857
EP  - 862
VL  - 336
IS  - 10
PB  - Elsevier
DO  - 10.1016/S1631-073X(03)00215-2
LA  - en
ID  - CRMATH_2003__336_10_857_0
ER  - 
%0 Journal Article
%A Amor Keziou
%T Dual representation of φ-divergences and applications
%J Comptes Rendus. Mathématique
%D 2003
%P 857-862
%V 336
%N 10
%I Elsevier
%R 10.1016/S1631-073X(03)00215-2
%G en
%F CRMATH_2003__336_10_857_0
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/

[1] M. Broniatowski, Estimation through Kullback–Leibler divergence, Math. Methods Statist. (2003) (submitted)

[2] N. Cressie; T. Read Multinomial goodness-of-fit tests, J. Roy. Statist. Soc. Ser. B, Volume 46 (1984) no. 3, pp. 440-464

[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

Cited by Sources:

Comments - Politique