Nonparametric estimation of an extreme-value copula in arbitrary dimensions

Journal of Multivariate Analysis

Volumn 102, Issue 1, 2011, Pages 37-47

  Gudendorf, Gordon ^a   Segers, Johan ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Empirical process; Linear regression; Minimum variance estimator; Multivariate extreme value distribution; Ordinary least squares; Pickands dependence function; Unit simplex

Indexed keywords

EID: 77957808302     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2010.07.011     Document Type: Article

References (21)

1. Capéraà P., Fougères A.-L. Estimation of a bivariate extreme value distribution. Extremes 2000, 3:311-329.
2. Capéraà P., Fougères A.-L., Genest C. A nonparametric estimation procedure for bivariate extreme value copulas. Biometrika 1997, 84:567-577.
3. Deheuvels P. Probabilistic aspects of multivariate extremes. Statistical Extremes and Applications 1984, 117-130. Reidel. J. Tiago de Oliveira (Ed.).
4. Deheuvels P. On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions. Statistics & Probability Letters 1991, 12(5):429-439.
5. Einmahl J.H.J., Segers J. Maximum empirical likelihood estimation of the spectral measure of an extreme-value distribution. The Annals of Statistics 2009, 37(5B):2953-2989.
6. Falk M., Reiss R. On pickands coordinates in arbitrary dimensions. Journal of Multivariate Analysis 2008, 92(2):426-453.
7. Fils-Villetard A., Guillou A., Segers J. Projection estimators of Pickands dependence functions. The Canadian Journal of Statistics 2008, 36(3):369-382.
8. Galambos J. The Asymptotic Theory of Extreme Order Statistics 1987, Krieger, Melbourne, Florida. 2nd ed.
9. Genest C., Segers J. Rank-based inference for bivariate extreme-value copulas. Annals of Statistics 2009, 37(5B):2990-3022.
10. Guillotte S., Perron F. A Bayesian estimator for the dependence function of a bivariate extreme-value distribution. The Canadian Journal of Statistics 2008, 36(3):383-396.
11. Hall P., Tajvidi N. Distribution and dependence-function estimation for bivariate extreme-value distributions. Bernoulli 2000, 6(5):835-844.
12. Jiménez J.R., Villa-Diharce E., Flores M. Nonparametric estimation of the dependence function in bivariate extreme value distributions. Journal of Multivariate Analysis 2001, 76(2):159-191.
13. Obretenov A. On the dependence function of Sibuya in multivariate extreme value theory. Journal of Multivariate Analysis 1991, 36(1):35-43.
14. J. Pickands, Multivariate extreme value distributions, in: Proceedings of the 43rd Session of the International Statistical Institute, vol. 2 (Buenos Aires, 1981) vol. 49, pp. 859-878, 894-902, with a discussion, 1981.
15. Segers J. Non-parametric inference for bivariate extreme-value copulas. Extreme Value Distributions 2007, 181-203. Nova Science Publishers, Inc., Older version available as CentER DP 2004-91, Tilburg University (Chapter 9). M. Ahsanulah, S. Kirmani (Eds.).
16. Stephenson A.G. Simulating multivariate extrme value analysis of logistic type. Extremes 2003, 6:49-59.
17. Stephenson A.G. EVD: extreme value distributions. R News 2002, 2(2). http://CRAN.R-project.org/doc/Rnews/.
18. Tawn J. Modelling Multivariate Extreme Vlaue Distributions. Biometrika 1990, 77(2):245-253.
19. van der Vaart A.W. Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics 1998, vol. 3. Cambridge University Press, Cambridge.
20. van der Vaart A.W., Wellner J.A. Weak Convergence and Empirical Processes. Cambridge Series in Statistical and Probabilistic Mathematics 1996, Springer, New York.
21. Zhang D., Wells M.T., Peng L. Nonparametric estimation of the dependence function for a multivariate extreme value distribution. Journal of Multivariate Analysis 2008, 99(4):577-588.