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.
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Amor Keziou 1
@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}, }
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] Multinomial goodness-of-fit tests, J. Roy. Statist. Soc. Ser. B, Volume 46 (1984) no. 3, pp. 440-464
[3] On topological properties of f-divergences, Studia Sci. Math. Hungar., Volume 2 (1967), pp. 329-339
[4] Large Deviations Techniques and Applications, Jones & Bartlett, 1998
[5] Convex Statistical Distances, Teubner, Leipzig, 1987
[6] Efficiency versus robustness: the case for minimum Hellinger distance and related methods, Ann. Statist., Volume 22 (1994), pp. 1081-1114
[7] Asymptotic divergence of estimates of discrete distributions, J. Statist. Plann. Inference, Volume 48 (1995) no. 3, pp. 347-369
[8] On the minimum discrimination information theorem, Statist. Decisions, Suppl., Volume 1 (1984), pp. 263-283
[9] Asymptotic Statistics, Cambridge Series in Statistical and Probabilitic Mathematics, 1998
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