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Weakening the independence assumption on polar components: limit theorems for generalized elliptical distributions

Published online by Cambridge University Press:  24 March 2016

Miriam Isabel Seifert
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Abstract

By considering the extreme behavior of bivariate random vectors with a polar representation R(u(T), v(T)), it is commonly assumed that the radial component R and the angular component T are stochastically independent. We investigate how to relax this rigid independence assumption such that conditional limit theorems can still be deduced. For this purpose, we introduce a novel measure for the dependence structure and present convenient criteria for validity of limit theorems possessing a geometrical meaning. Thus, our results verify a stability of the available limit results, which is essential in applications where the independence of the polar components is not necessarily present or exactly fulfilled.

Keywords

Conditional extreme value modelpolar representationelliptical distributionGumbel max-domain of attractionrandom norming
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 130 - 145
Copyright
Copyright © Applied Probability Trust 2016 

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