MAXIMUM EMPIRICAL LIKELIHOOD ESTIMATION OF THE SPECTRAL MEASURE OF AN EXTREME-VALUE DISTRIBUTION
成果类型：
Article
署名作者：
Einmahl, John H. J.; Segers, Johan
署名单位：
Tilburg University; Universite Catholique Louvain
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/08-AOS677
发表日期：
2009
页码：
2953-2989
关键词：
摘要：
Consider a random sample from a bivariate distribution function F in the max-domain of attraction of all extreme-value distribution function G. This G is characterized by two extreme-value indices and a spectral measure, the latter determining the tail dependence structure of F. A major issue in multivariate extreme-value theory is the estimation of the spectral measure (1)p with respect to the L-p norm. For every p is an element of [1, infinity], a nonparametric maximum empirical likelihood estimator is proposed for Phi(p). The main novelty is that these estimators are guaranteed to satisfy the moment constraints by which spectral measures are characterized. Asymptotic normality of the estimators is proved under conditions that allow for tail independence. Moreover, the conditions are easily verifiable as we demonstrate through a number of theoretical examples. A simulation study shows a substantially improved performance of the new estimators. Two case Studies illustrate how to implement the methods in practice.
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