no. 7-8
Statistics
A semiparametric test of independence in copula models for censored data
[Test d'indépendance semiparamétrique dans des modèles de copule pour les données censurées]

Présenté par : Wendelin Werner

Bouzebda, Salim1 ; Keziou, Amor1, 2
1 LSTA-université Paris 6, 175, rue du Chevaleret, boîte 158, 75013 Paris, France
2 Laboratoire de mathématiques (FRE 3111) CNRS, université de Reims, Reims, France
Comptes Rendus. Mathématique, Tome 348 (2010) no. 7-8, pp. 449-453.

Nous proposons un test d'indépendance dans des modèles de copule dans le cadre des données censurées. Nous obtenons les lois asymptotiques, de l'estimateur et de la statistique de test proposés, lorsque le paramètre est un point frontière de son domaine.

We propose a semiparametric test of independence in copula models for bivariate survival censored data. We give the limit laws of the estimate of the parameter and the proposed test statistic under the null hypothesis of independence.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.02.013
Bouzebda, Salim 1 ; Keziou, Amor 1, 2

1 LSTA-université Paris 6, 175, rue du Chevaleret, boîte 158, 75013 Paris, France
2 Laboratoire de mathématiques (FRE 3111) CNRS, université de Reims, Reims, France 
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Bouzebda, Salim; Keziou, Amor. A semiparametric test of independence in copula models for censored data. Comptes Rendus. Mathématique, Tome 348 (2010) no. 7-8, pp. 449-453. doi : 10.1016/j.crma.2010.02.013. http://www.numdam.org/articles/10.1016/j.crma.2010.02.013/

[1] Andrews, D.W.K. Estimation when a parameter is on a boundary, Econometrica, Volume 67 (1999) no. 6, pp. 1341-1383

[2] Bouzebda, S.; Keziou, A. A test of independence in some copula models, Math. Methods Statist., Volume 17 (2008) no. 2, pp. 123-137

[3] Bouzebda, S.; Keziou, A. A new test procedure of independence in copula models via χ2-divergence, Comm. Statist. Theory Methods, Volume 39 (2010) no. 1, pp. 1-20

[4] Chant, D. On asymptotic tests of composite hypotheses in nonstandard conditions, Biometrika, Volume 61 (1974), pp. 291-298

[5] Chernoff, H. On the distribution of the likelihood ratio, Ann. Math. Statist., Volume 25 (1954), pp. 573-578

[6] Genest, C.; Ghoudi, K.; Rivest, L.-P. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika, Volume 82 (1995) no. 3, pp. 543-552

[7] Joe, H. Parametric families of multivariate distributions with given margins, J. Multivariate Anal., Volume 46 (1993) no. 2, pp. 262-282

[8] Joe, H. Multivariate Models and Dependence Concepts, Monogr. Statist. Appl. Probab., vol. 73, Chapman & Hall, London, 1997

[9] Kaplan, E.L.; Meier, P. Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc., Volume 53 (1958), pp. 457-481

[10] Kimeldorf, G.; Sampson, A. One-parameter families of bivariate distributions with fixed marginals, Comm. Statist., Volume 4 (1975), pp. 293-301

[11] Kimeldorf, G.; Sampson, A. Uniform representations of bivariate distributions, Comm. Statist., Volume 4 (1975) no. 7, pp. 617-627

[12] Moran, P.A.P. Maximum-likelihood estimation in non-standard conditions, Proc. Cambridge Philos. Soc., Volume 70 (1971), pp. 441-450

[13] Nelsen, R.B. An Introduction to Copulas, Lecture Notes in Statist., vol. 139, Springer-Verlag, New York, 1999

[14] Oakes, D. Multivariate survival distributions, J. Nonparametr. Stat., Volume 3 (1994) no. 3–4, pp. 343-354

[15] Self, S.G.; Liang, K.-Y. Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions, J. Amer. Statist. Assoc., Volume 82 (1987) no. 398, pp. 605-610

[16] Shih, J.H.; Louis, T.A. Inferences on the association parameter in copula models for bivariate survival data, Biometrics, Volume 51 (1995) no. 4, pp. 1384-1399

[17] Tsukahara, H. Semiparametric estimation in copula models, Canad. J. Statist., Volume 33 (2005) no. 3, pp. 357-375

[18] Wang, W.; Ding, A.A. On assessing the association for bivariate current status data, Biometrika, Volume 87 (2000) no. 4, pp. 879-893

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