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On Kesten's counterexample to the Cramer-Wold device for regular variation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0001-9210-121X
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2006 (English)In: Bernoulli, ISSN 1350-7265, Vol. 12, no 1, 133-142 p.Article in journal (Refereed) Published
Abstract [en]

In 2002 Basrak, Davis and Mikosch showed that an analogue of the Cramer-Wold device holds for regular variation of random vectors if the index of regular variation is not an integer. This characterization is of importance when studying stationary solutions to stochastic recurrence equations. In this paper we construct counterexamples showing that for integer-valued indices, regular variation of all linear combinations does not imply that the vector is regularly varying. The construction is based on unpublished notes by Harry Kesten.

Place, publisher, year, edition, pages
2006. Vol. 12, no 1, 133-142 p.
Keyword [en]
heavy-tailed distributions, linear combinations, multivariate regular, variation, stationary distribution, tail
National Category
Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-15537ISI: 000236189900008ScopusID: 2-s2.0-33646099676OAI: diva2:333578

QC 20141127

Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2015-09-01Bibliographically approved

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