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Dependence of Multivariate Extremes

  • C. Viseu
  • L. Pereira
  • A. P. Martins
  • H. Ferreira
Conference paper
Part of the Studies in Theoretical and Applied Statistics book series (STAS)

Abstract

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.

Notes

Acknowledgements

The authors thank the referees for all the helpful remarks. This research was supported by the research unit “Centro de Matemática” of the University of Beira Interior through the Foundation for Science and Technology (FCT).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • C. Viseu
    • 1
  • L. Pereira
    • 2
  • A. P. Martins
    • 2
  • H. Ferreira
    • 2
  1. 1.Polytechnic Institute of CoimbraCoimbraPortugal
  2. 2.University of Beira InteriorCovilhãPortugal

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