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Dependence of Multivariate Extremes

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Book cover Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications

Part of the book series: Studies in Theoretical and Applied Statistics ((STASSPSS))

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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.

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References

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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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Authors and Affiliations

  1. Polytechnic Institute of Coimbra, Coimbra, Portugal

    C. Viseu

  2. University of Beira Interior, Covilhã, Portugal

    L. Pereira, A. P. Martins & H. Ferreira

Authors
  1. C. Viseu
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  2. L. Pereira
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  3. A. P. Martins
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  4. H. Ferreira
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Corresponding author

Correspondence to C. Viseu .

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Editors and Affiliations

  1. , Universidade Nova de Lisboa, CMA and Faculdade de Ciˆenciase Tecnolog, Caparica, Caparica, 2829-516, Portugal

    João Lita da Silva

  2. , Universidade Nova de Lisboa, CMA and Faculdade de Ciˆenciase Tecnolog, Caparica, Caparica, 2829-516, Portugal

    Frederico Caeiro

  3. , Universidade Nova de Lisboa, CEAUL and Faculdade de Ciˆenciase Tecnol, Caparica, Caparica, 2829-516, Portugal

    Isabel Natário

  4. , Universidade Nova de Lisboa,, CEAUL and Faculdade de Ciˆenciase Tecnol, Caparica 59, Caparica, 2829-516, Portugal

    Carlos A. Braumann

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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. https://doi.org/10.1007/978-3-642-34904-1_49

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