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Dependence Measures for Extreme Value Analyses
Authors:Stuart Coles  Janet Heffernan  Jonathan Tawn
Institution:(1) Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK
Abstract:Quantifying dependence is a central theme in probabilistic and statistical methods for multivariate extreme values. Two situations are possible: one where, in a limiting sense, the extremes are dependent; the other where, in the same sense, the extremes are independent. This paper comprises an overview of the principal issues through a unified approach which encompasses both these situations. Novel diagnostic measures for dependence are also developed which provide complementary information about different aspects of extremal dependence. The paper is written in an elementary style, with the methodology illustrated by application to theoretical examples and typical data-sets. These data-sets and the S-plus functions used for the analyses are available online.
Keywords:asymptotic independence  bivariate extreme value distribution  copula  point processes
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