Inequalities for the extremal coefficients of multivariate extreme value distributions

Schlather, Martin ; Tawn, Jonathan A.

Document Type: Article
Year of publication: 2002
The title of a journal, publication series: Extremes : Statistical Theory and Applications in Science, Engineering and Economics
Volume: 5
Issue number: 1
Page range: 87-102
Place of publication: Dordrecht [u.a.]
Publishing house: Springer Science + Business Media
ISSN: 1386-1999
Publication language: English
Institution: School of Business Informatics and Mathematics > Mathematische Statistik (Schlather 2012-)
Subject: 510 Mathematics
Keywords (English): dependence measures, extremal coefficient, multivariate extreme value distribution, inequalities, self-consistency
Abstract: The extremal coefficients are the natural dependence measures for multivariate extreme value distributions. For an m-variate distribution 2m distinct extremal coefficients of different orders exist; they are closely linked and therefore a complete set of 2m coefficients cannot take any arbitrary values. We give a full characterization of all the sets of extremal coefficients. To this end, we introduce a simple class of extreme value distributions that allows for a 1-1 mapping to the complete sets of extremal coefficients. We construct bounds that higher order extremal coefficients need to satisfy to be consistent with lower order extremal coefficients. These bounds are useful as lower order extremal coefficients are the most easily inferred from data.

Dieser Datensatz wurde nicht während einer Tätigkeit an der Universität Mannheim veröffentlicht, dies ist eine Externe Publikation.

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