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Zbl 1043.62048
Wüthrich, Mario V.
Bivariate extension of the Pickands-Balkema-de Haan theorem. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 40, No. 1, 33-41 (2004). ISSN 0246-0203

Summary: We prove a two-dimensional version of the famous Pickands-Balkema-de Haan theorem of extreme value theory [see {\it J. Pickands}, Ann. Stat. 3, 119--131 (1975; Zbl 0312.62038); {\it A. A. Balkema} and {\it L. de Haan}, Ann. Probab. 2, 792--804 (1974; Zbl 0295.60014)]. The bivariate random variables are generated using the copula language. This representation of dependence structures allows to derive asymptotic results for bivariate excess distributions.

MSC 2000:: *62H05 Multivariate structure theory
62E20 Asymptotic distribution theory in statistics
62H20 Statistical measures of associations

Keywords: Archimedean copula; Dependent random variables; Extreme value theory; Pickands-Balkema-de Haan theorem

Citations: Zbl 0312.62038; Zbl 0295.60014

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