Geodesic
Semiparametric estimation of the parameters of multivariate copulas
Kybernetika, Tome 45 (2009) no. 6, pp. 972-991 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In the paper we investigate properties of maximum pseudo-likelihood estimators for the copula density and minimum distance estimators for the copula. We derive statements on the consistency and the asymptotic normality of the estimators for the parameters.
In the paper we investigate properties of maximum pseudo-likelihood estimators for the copula density and minimum distance estimators for the copula. We derive statements on the consistency and the asymptotic normality of the estimators for the parameters.
Classification : 62G07, 62G20, 62H12
Keywords: multivariate density estimation; copula; maximum likelihood estimators; minimum distance estimators 
@article{KYB_2009_45_6_a6,
     author = {Liebscher, Eckhard},
     title = {Semiparametric estimation of the parameters of multivariate copulas},
     journal = {Kybernetika},
     pages = {972--991},
     year = {2009},
     volume = {45},
     number = {6},
     mrnumber = {2650077},
     zbl = {1186.62076},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2009_45_6_a6/}
}
TY  - JOUR
AU  - Liebscher, Eckhard
TI  - Semiparametric estimation of the parameters of multivariate copulas
JO  - Kybernetika
PY  - 2009
SP  - 972
EP  - 991
VL  - 45
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/KYB_2009_45_6_a6/
LA  - en
ID  - KYB_2009_45_6_a6
ER  - 
%0 Journal Article
%A Liebscher, Eckhard
%T Semiparametric estimation of the parameters of multivariate copulas
%J Kybernetika
%D 2009
%P 972-991
%V 45
%N 6
%U http://geodesic.mathdoc.fr/item/KYB_2009_45_6_a6/
%G en
%F KYB_2009_45_6_a6
Liebscher, Eckhard. Semiparametric estimation of the parameters of multivariate copulas. Kybernetika, Tome 45 (2009) no. 6, pp. 972-991. http://geodesic.mathdoc.fr/item/KYB_2009_45_6_a6/

[1] X. Chen and Y. Fan: Pseudo-likelihood ratio tests for semiparametric multivariate copula model selection. Canad. J. Statist. 33 (2005), 389–414. | MR

[2] X. Chen and Y. Fan: Estimation of copula-based semiparametric time series models. J. Econometrics 130 (2006), 307–335. | MR

[3] X. Chen and Y. Fan, and V. Tsyrennikov: Efficient estimation of semiparametric multivariate copula models. J. Amer. Statist. Assoc. 101 (2006), 1228–1240. | MR

[4] J.-D. Fermanian: Goodness-of-fit tests for copulas. J. Multivariate Anal. 95 (2005), 119–152. | MR | Zbl

[5] C. Genest, K. Ghoudi, and L.-P. Rivest: A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82 (1995), 543–552. | MR

[6] C. Genest, J.-F. Quessy, and B. Rémillard: Goodness-of-fit procedures for copula models based on the probability integral transformation. Scand. J. Statist. 33 (2006), 337–366. | MR

[7] C. Genest and L.-P. Rivest: Statistical inference procedures for bivariate Archimedian copulas. J. Amer. Statist. Assoc. 88 (1993), 1034–1043. | MR

[8] C. Genest and B. J. M. Werker: Conditions for the asymptotic efficiency of an omnibus estimator of dependence estimators in copula models. In: Distributions with Given Marginals and Statistical Modelling (C. M. Cuadras et al., eds.), Kluwer, Dordrecht 2000, pp. 103–112. | MR

[9] I. Gijbels and J. Mielniczuk: Estimating the density of a copula function. Comm. Statist. – Theory Methods 19 (1990), 445–464. | MR

[10] P. Hall and N. Neumayer: Estimating a bivariate density when there are extra data on one or both components. Working Paper, 2006.

[11] C. Hess: Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator. Ann. Statist. 24 (1996), 1298–1315. | MR | Zbl

[12] H. Joe: Multivariate Models and Dependence Concepts. Chapman and Hall, London 1997. | MR | Zbl

[13] H. Joe: Asymptotic efficiency of the two-stage estimation method for copula-based models. J. Multivariate Anal. 94 (2005), 401–419. | MR | Zbl

[14] P. Lachout, E. Liebscher, and S. Vogel: Strong convergence of estimators as $\varepsilon _{n}$-minimisers of optimisation problems. Ann. Inst. Statist. Math. 57 (2005), 291–313. | MR

[15] E. Liebscher: Semiparametric density estimators using copulas. Comm. Statist. – Theory Methods 34 (2005), 59–71. | MR | Zbl

[16] E. Liebscher: Construction of asymmetric multivariate copulas. J. Multivariate Anal. 99 (2008), 2234–2250. | MR | Zbl

[17] R. B. Nelsen: An Introduction to Copulas. (Lecture Notes in Statistics 139.) Springer, New York 1999. | MR | Zbl

[18] D. Oakes: Multivariate Survival distributions. J. Nonparametric Statist. 3 (1994), 343–354. | MR

[19] R. Serfling: Approximation Theorems of Mathematical Statistics. Wiley, New York 1980. | MR | Zbl

[20] J. H. Shih and T. A. Louis: Inferences on the association parameter in copula models for bivariate survival data. Biometrics 55 (1995), 1384–1399. | MR

[21] A. Suzukawa, H. Imai, and Y. Sato: Kullback–Leibler information consistent estimation for censored data. Ann. Inst. Statist. Math. 53 (2001), 262–276. | MR

[22] H. Tsukahara: Semiparametric estimation in copula models. Canad. J. Statist. 33 (2005), 357–375. | MR | Zbl

[23] W. Wang and M. T. Wells: Model selection and semiparametric inference for bivariate failure-time data. J. Amer. Statist. Assoc. 95 (2000), 62–76. | MR