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Measures of multivariate asymptotic dependence and their relation to spectral expansions

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  • Melanie Frick

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    Abstract

    Asymptotic dependence can be interpreted as the property that realizations of the single components of a random vector occur simultaneously with a high probability. Information about the asymptotic dependence structure can be captured by dependence measures like the tail dependence parameter or the residual dependence index. We introduce these measures in the bivariate framework and extend them to the multivariate case afterwards. Within the extreme value theory one can model asymptotic dependence structures by Pickands dependence functions and spectral expansions. Both in the bivariate and in the multivariate case we also compute the tail dependence parameter and the residual dependence index on the basis of this statistical model. They take a specific shape then and are related to the Pickands dependence function and the exponent of variation of the underlying density expansion. Copyright Springer-Verlag 2012

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    Bibliographic Info

    Article provided by Springer in its journal Metrika.

    Volume (Year): 75 (2012)
    Issue (Month): 6 (August)
    Pages: 819-831

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    Handle: RePEc:spr:metrik:v:75:y:2012:i:6:p:819-831

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    Related research

    Keywords: Asymptotic dependence structure; Tail dependence parameter; Residual dependence index; Spectral expansion; Pickands dependence function;

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    1. Frick, Melanie & Reiss, Rolf-Dieter, 2009. "Expansions of multivariate Pickands densities and testing the tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1168-1181, July.
    2. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate conditional versions of Spearman's rho and related measures of tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1123-1140, July.
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    Cited by:
    1. Nolde, Natalia, 2014. "Geometric interpretation of the residual dependence coefficient," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 85-95.

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