| Title:
|
Semiparametric estimation of the parameters of multivariate copulas (English) |
| Author:
|
Liebscher, Eckhard |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
6 |
| Year:
|
2009 |
| Pages:
|
972-991 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
multivariate density estimation |
| Keyword:
|
copula |
| Keyword:
|
maximum likelihood estimators |
| Keyword:
|
minimum distance estimators |
| MSC:
|
62G07 |
| MSC:
|
62G20 |
| MSC:
|
62H12 |
| idZBL:
|
Zbl 1186.62076 |
| idMR:
|
MR2650077 |
| . |
| Date available:
|
2010-06-02T19:28:48Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140022 |
| . |
| Reference:
|
[1] X. Chen and Y. Fan: Pseudo-likelihood ratio tests for semiparametric multivariate copula model selection.Canad. J. Statist. 33 (2005), 389–414. MR 2193982 |
| Reference:
|
[2] X. Chen and Y. Fan: Estimation of copula-based semiparametric time series models.J. Econometrics 130 (2006), 307–335. MR 2211797 |
| Reference:
|
[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 2328309 |
| Reference:
|
[4] J.-D. Fermanian: Goodness-of-fit tests for copulas.J. Multivariate Anal. 95 (2005), 119–152. Zbl 1095.62052, MR 2164126 |
| Reference:
|
[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 1366280 |
| Reference:
|
[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 2279646 |
| Reference:
|
[7] C. Genest and L.-P. Rivest: Statistical inference procedures for bivariate Archimedian copulas.J. Amer. Statist. Assoc. 88 (1993), 1034–1043. MR 1242947 |
| Reference:
|
[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 2058984 |
| Reference:
|
[9] I. Gijbels and J. Mielniczuk: Estimating the density of a copula function.Comm. Statist. – Theory Methods 19 (1990), 445–464. MR 1067582 |
| Reference:
|
[10] P. Hall and N. Neumayer: Estimating a bivariate density when there are extra data on one or both components.Working Paper, 2006. |
| Reference:
|
[11] C. Hess: Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator.Ann. Statist. 24 (1996), 1298–1315. Zbl 0862.62029, MR 1401851 |
| Reference:
|
[12] H. Joe: Multivariate Models and Dependence Concepts.Chapman and Hall, London 1997. Zbl 0990.62517, MR 1462613 |
| Reference:
|
[13] H. Joe: Asymptotic efficiency of the two-stage estimation method for copula-based models.J. Multivariate Anal. 94 (2005), 401–419. Zbl 1066.62061, MR 2167922 |
| Reference:
|
[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 2160652 |
| Reference:
|
[15] E. Liebscher: Semiparametric density estimators using copulas.Comm. Statist. – Theory Methods 34 (2005), 59–71. Zbl 1066.62046, MR 2162520 |
| Reference:
|
[16] E. Liebscher: Construction of asymmetric multivariate copulas.J. Multivariate Anal. 99 (2008), 2234–2250. Zbl 1151.62043, MR 2463386 |
| Reference:
|
[17] R. B. Nelsen: An Introduction to Copulas.(Lecture Notes in Statistics 139.) Springer, New York 1999. Zbl 1152.62030, MR 1653203 |
| Reference:
|
[18] D. Oakes: Multivariate Survival distributions.J. Nonparametric Statist. 3 (1994), 343–354. MR 1291555 |
| Reference:
|
[19] R. Serfling: Approximation Theorems of Mathematical Statistics.Wiley, New York 1980. Zbl 1001.62005, MR 0595165 |
| Reference:
|
[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 1381050 |
| Reference:
|
[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 1841135 |
| Reference:
|
[22] H. Tsukahara: Semiparametric estimation in copula models.Canad. J. Statist. 33 (2005), 357–375. Zbl 1077.62022, MR 2193980 |
| Reference:
|
[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 1803141 |
| . |
