The space of D-norms revisited

The theory of D -norms is an offspring of multivariate extreme value theory. We present recent results on D -norms, which are completely determined by a certain random vector called generator. In the first part it is shown that the space of D -norms is a complete separable metric space, if equipped...

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Veröffentlicht in:Extremes (Boston) 2015-03, Vol.18 (1), p.85-97
Hauptverfasser: Aulbach, Stefan, Falk, Michael, Zott, Maximilian
Format: Artikel
Sprache:eng
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Zusammenfassung:The theory of D -norms is an offspring of multivariate extreme value theory. We present recent results on D -norms, which are completely determined by a certain random vector called generator. In the first part it is shown that the space of D -norms is a complete separable metric space, if equipped with the Wasserstein-metric in a suitable way. Secondly, multiplying a generator with a doubly stochastic matrix yields another generator. An iteration of this multiplication provides a sequence of D -norms and we compute its limit. Finally, we consider a parametric family of D -norms, where we assume that the generator follows a symmetric Dirichlet distribution. This family covers the whole range between complete dependence and independence.
ISSN:1386-1999
1572-915X
DOI:10.1007/s10687-014-0204-y