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

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 Author Das, Bikramjit ♦ Resnick, Sidney I. Source arXiv.org Content type Text File Format PDF Date of Submission 2008-05-28 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics ♦ Probabilities & applied mathematics Subject Keyword Mathematics - Probability ♦ Mathematics - Statistics Theory ♦ math ♦ stat 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 $[0,\infty]\times(0,\infty]$. Description Reference: Bernoulli 2011, Vol. 17, No. 1, 226-252 Educational Use Research Learning Resource Type Article