Skip Navigation

Biometrika 1997 84(3):567-577; doi:10.1093/biomet/84.3.567
© 1997 by Biometrika Trust
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by CAPÉRAÀ, P.
Right arrow Articles by GENEST, C.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

A nonparametric estimation procedure for bivariate extreme value copulas

P. CAPÉRAÀ, A.-L. FOUGÈRES and C. GENEST

Département de mathématiques et de statistique, Université Laval Québec, Canada G1K 7P4 e-mail: caperaa{at}mat.ulaval.ca fougeres{at}mat.ulaval.ca genest{at}mat.ulaval.ca

A bivariate extreme value distribution with fixed marginals is generated by a one-dimensional map called a dependence function. This paper proposes a new nonparametric estimator of this function. Its asymptotic properties are examined, and its small-sample behaviour is compared to that of other rank-based and likelihood-based procedures. The new estimator is shown to be uniformly, strongly convergent and asymptotically unbiased. Through simulations, it is also seen to perform reasonably well against the maximum likelihood estimator based on the correct model and to have smaller L1, L2 and L{infty} errors than any existing nonparametric alternative. The n½ consistency of the proposed estimator leads to nonparametric estimation of Tawn's (1988) dependence measure that may be used to test independence in small samples.

Key Words: Asymptotic theory • Copula • Dependence function • Extreme value distribution • Nonparametric estimation


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.