Dependence of Multivariate Extremes
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- Viseu C., Pereira L., Martins A.P., Ferreira H. (2013) Dependence of Multivariate Extremes. In: Lita da Silva J., Caeiro F., Natário I., Braumann C. (eds) Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics. Springer, Berlin, Heidelberg
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.