Nonparametric estimation of the dependence function for a multivariate extreme value distribution

JOURNAL OF MULTIVARIATE ANALYSIS

卷:99

Article

Zhang, Dabao³  Wells, Martin T.^1,2  Peng, Liang⁴ 

[1] Cornell Univ, Dept Stat Sci, Ithaca, NY 14853 USA

[2] Cornell Univ, Dept Biol Stat & Comp Biol, Ithaca, NY 14853 USA

[3] Purdue Univ, Dept Stat, W Lafayette, IN 47907 USA

[4] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

关键词: copulas;    dependence function;    empirical distribution;    Gaussian process;    multivariate extreme value distribution;   

DOI  :  10.1016/j.jmva.2006.09.011

来源: Elsevier

【 摘 要 】

Understanding and modeling dependence structures for multivariate extreme values are of interest in a number of application areas. One of the well-known approaches is to investigate the Pickands dependence function. In the bivariate setting, there exist several estimators for estimating the Pickands dependence function which assume known marginal distributions [J. Pickands, Multivariate extreme value distributions, Bull. Internat. Statist. Inst., 49 (1981) 859-878; P. Deheuvels, On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions, Statist. Probab. Lett. 12 (1991) 429-439; P. Hall, N. Tajvidi, Distribution and dependence-function estimation for bivariate extreme-value distributions, Bernoulli 6 (2000) 835-844; P. Caperaa,A.-L. Fougeres, C. Genest,A nonparametric estimation procedure for bivariate extreme value copulas, Biometrika 84 (1997) 567-577]. In this paper, we generalize the bivariate results to p-variate multivariate extreme value distributions with p >= 2. We demonstrate that the proposed estimators are consistent and asymptotically normal as well as have excellent small sample behavior. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free