Conditional independence and conditioned limit laws

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Conditioned limit laws constitute an important and well developed framework of extreme value theory that describe a broad range of extremal dependence forms including asymptotic independence. We explore the assumption of conditional independence of X1 and X2 given X0 and study its implication in the limiting distribution of (X1;X2) conditionally on X0 being large. We show that under random norming, conditional independence is always preserved in the conditioned limit law but might fail to do so when the normalisation does not include the precise value of the random variable in the conditioning event.
Original languageEnglish
Pages (from-to)1-4
JournalStatistics and Probability Letters
Early online date14 Jan 2016
Publication statusPublished - May 2016


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