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Modelling dependence within joint tail regions. (English) Zbl 0886.62063
Summary: Standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max-stability, a particular form of joint tail dependence. We develop joint tail models based on a broader class of dependence structure which provides a natural link between max-stable models and weaker forms of dependence including independence and negative association. This approach overcomes many of the problems that are encountered with standard methods and is the basis for a Poisson process representation that generalizes existing bivariate results. We apply the new techniques to simulated and environmental data, and demonstrate the marked advantage that the new approach offers for joint tail extrapolation.

62H20 Measures of association (correlation, canonical correlation, etc.)
62H99 Multivariate analysis
62H05 Characterization and structure theory for multivariate probability distributions; copulas