[Estimation et tests d'indépendance dans des modèles de copules via les divergences]
Nous introduisons de nouveaux estimateurs et tests d'indépendance dans des modèles de copule avec des marges inconnues en utilisant les divergences entre copules et la technique de dualité. Nous obtenons les lois asymptotiques, des estimateurs et des statistiques de tests proposés, lorsque le paramètre est un point intérieur ou un point frontière de son domaine.
We introduce new estimates and tests of independence in copula models with unknown margins using ϕ-divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior point or not.
Accepté le :
Publié le :
@article{CRMATH_2009__347_11-12_667_0,
author = {Salim Bouzebda and Amor Keziou},
title = {Estimation and tests of independence in copula models via divergences},
journal = {Comptes Rendus. Math\'ematique},
pages = {667--672},
publisher = {Elsevier},
volume = {347},
number = {11-12},
year = {2009},
doi = {10.1016/j.crma.2009.03.016},
language = {en},
}
Salim Bouzebda; Amor Keziou. Estimation and tests of independence in copula models via divergences. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 667-672. doi : 10.1016/j.crma.2009.03.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.03.016/
[1] A test of independence in some copula models, Math. Methods Statist., Volume 17 (2008) no. 2, pp. 123-137
[2] Parametric estimation and tests through divergences and the duality technique, J. Multivariate Anal., Volume 100 (2009) no. 1, pp. 16-36
[3] Minimization of ϕ-divergences on sets of signed measures, Studia Sci. Math. Hungar., Volume 43 (2006) no. 4, pp. 403-442
[4] Propriétés d'existence et propriétés topologiques des fonctions de dépendance avec applications à la convergence des types pour des lois multivariées, C. R. Acad. Sci. Paris, Sér. A–B, Volume 288 (1979) no. 2, p. A145-A148
[5] Nonparametric test of independence, Nonparametric Asymptotic Statistics (Proc. Conf., Rouen, 1979) (French), Lecture Notes in Math., vol. 821, Springer, Berlin, 1980, pp. 95-107
[6] A Kolmogorov–Smirnov type test for independence and multivariate samples, Rev. Roumaine Math. Pures Appl., Volume 26 (1981) no. 2, pp. 213-226
[7] A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika, Volume 82 (1995) no. 3, pp. 543-552
[8] Parametric families of multivariate distributions with given margins, J. Multivariate Anal., Volume 46 (1993) no. 2, pp. 262-282
[9] Multivariate Models and Dependence Concepts, Monographs on Statistics and Applied Probability, vol. 73, Chapman & Hall, London, 1997
[10] Dual representation of ϕ-divergences and applications, C. R. Math. Acad. Sci. Paris, Volume 336 (2003) no. 10, pp. 857-862
[11] Convex Statistical Distances, vol. 95, BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 1987
[12] An Introduction to Copulas, Lecture Notes in Statistics, vol. 139, Springer-Verlag, New York, 1999
[13] Multivariate survival distributions, J. Nonparametr. Statist., Volume 3 (1994) no. 3–4, pp. 343-354
[14] Asymptotic normality of nonparametric tests for independence, Ann. Statist., Volume 2 (1974), pp. 892-910
[15] Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris, Volume 8 (1959), pp. 229-231
[16] Semiparametric estimation in copula models, Canad. J. Statist., Volume 33 (2005) no. 3, pp. 357-375
[17] On assessing the association for bivariate current status data, Biometrika, Volume 87 (2000) no. 4, pp. 879-893
Cité par Sources :
Commentaires - Politique
A semiparametric test of independence in copula models for censored data
Salim Bouzebda; Amor Keziou
C. R. Math (2010)
Robustness of dual divergence estimators for models satisfying linear constraints
Aida Toma
C. R. Math (2013)
Test of homogeneity in semiparametric two-sample density ratio models
Amor Keziou; Samuela Leoni-Aubin
C. R. Math (2005)