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Dependence of multivariate extremes

Viseu, C. ; Pereira, L.; Martins, A. P.; Ferreira, Helena

Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications, Studies in Theoretical and Applied Statistics, Springer Berlin Heidelberg, (2013), 463-471

We give necessary and sufficient conditions for two sub-vectors of a random vector with a multivariate extreme value (MEV) distribution, corresponding to the limit distribution of the maximum of a multidimensional stationary sequence with extremal index, to be independent or totally dependent. Those conditions involve first relations between the multivariate extremal indices of the sequences and secondly a coefficient that measures the strength of dependence between both sub-vectors. The main results are illustrated with an auto-regressive sequence and a 3-dependent sequence.