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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  and further studied by Heffernan and Resnick . These papers left unresolved the consistency of differentdoi:10.3150/10-bej271 fatcat:ahvqvytasjhuzekedfeo7635km