Open Access
February 2011 Conditioning on an extreme component: Model consistency with regular variation on cones
Bikramjit Das, Sidney I. Resnick
Bernoulli 17(1): 226-252 (February 2011). DOI: 10.3150/10-BEJ271

Abstract

Multivariate extreme value theory assumes a multivariate domain of attraction condition for the distribution of a random vector. This necessitates that each component satisfies a marginal domain of attraction condition. An approximation of the joint distribution of a random vector obtained by conditioning on one of the components being extreme was developed by Heffernan and Tawn [12] and further studied by Heffernan and Resnick [11]. These papers left unresolved the consistency of different models obtained by conditioning on different components being extreme and we here provide clarification of this issue. We also clarify the relationship between these conditional distributions, multivariate extreme value theory and standard regular variation on cones of the form $[0, ∞]×(0, ∞]$.

Citation

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Bikramjit Das. Sidney I. Resnick. "Conditioning on an extreme component: Model consistency with regular variation on cones." Bernoulli 17 (1) 226 - 252, February 2011. https://doi.org/10.3150/10-BEJ271

Information

Published: February 2011
First available in Project Euclid: 8 February 2011

zbMATH: 1284.60103
MathSciNet: MR2797990
Digital Object Identifier: 10.3150/10-BEJ271

Keywords: Asymptotic independence , Conditional extreme value model , domain of attraction , regular variation

Rights: Copyright © 2011 Bernoulli Society for Mathematical Statistics and Probability

Vol.17 • No. 1 • February 2011
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