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

Dabao Zhang, Martin T. Wells and Liang Peng

Journal of Multivariate Analysis, 2008, vol. 99, issue 4, 577-588

Abstract: 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. Capéraà, A.-L. Fougères, 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[greater-or-equal, slanted]2. We demonstrate that the proposed estimators are consistent and asymptotically normal as well as have excellent small sample behavior.

Keywords: Copulas; Dependence; function; Empirical; distribution; Gaussian; process; Multivariate; extreme; value; distribution (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (9)

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