Bernoulli

  • Bernoulli
  • Volume 17, Number 1 (2011), 226-252.

Conditioning on an extreme component: Model consistency with regular variation on cones

Bikramjit Das and Sidney I. Resnick

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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 $[0, ∞]×(0, ∞]$.

Article information

Source
Bernoulli, Volume 17, Number 1 (2011), 226-252.

Dates
First available in Project Euclid: 8 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.bj/1297173841

Digital Object Identifier
doi:10.3150/10-BEJ271

Mathematical Reviews number (MathSciNet)
MR2797990

Zentralblatt MATH identifier
1284.60103

Keywords
asymptotic independence conditional extreme value model domain of attraction regular variation

Citation

Das, Bikramjit; Resnick, Sidney I. Conditioning on an extreme component: Model consistency with regular variation on cones. Bernoulli 17 (2011), no. 1, 226--252. doi:10.3150/10-BEJ271. https://projecteuclid.org/euclid.bj/1297173841


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