ASYMPTOTIC DEPENDENCE FOR LIGHT-TAILED HOMOTHETIC DENSITIES

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ASYMPTOTIC DEPENDENCE FOR LIGHT-TAILED HOMOTHETIC DENSITIES

TitleASYMPTOTIC DEPENDENCE FOR LIGHT-TAILED HOMOTHETIC DENSITIES
Publication TypeJournal Article
Year of Publication2012
AuthorsBalkema, G, Nolde, N
JournalADVANCES IN APPLIED PROBABILITY
Volume44
Pagination506-527
Date PublishedJUN
Type of ArticleArticle
ISSN0001-8678
KeywordsAsymptotic dependence, Geometric approach, homothetic level set, light-tailed density, multivariate extreme
AbstractDependence between coordinate extremes is a key factor in any multivariate risk assessment. Hence, it is of interest to know whether the components of a given multivariate random vector exhibit asymptotic independence or asymptotic dependence. In the latter case the structure of the asymptotic dependence has to be clarified. In the multivariate setting it is common to have an explicit form of the density rather than the distribution function. In this paper we therefore give criteria for asymptotic dependence in terms of the density. We consider distributions with light tails and restrict attention to continuous unimodal densities defined on the whole space or on an open convex cone. For simplicity, the density is assumed to be homothetic: all level sets have the same shape. Balkema and Nolde (2010) contains conditions on the shape which guarantee asymptotic independence. The situation for asymptotic dependence, treated in the present paper, is more delicate.