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Conditional independence and conditioned limit laws

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  • Papastathopoulos, Ioannis

Abstract

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.

Suggested Citation

  • Papastathopoulos, Ioannis, 2016. "Conditional independence and conditioned limit laws," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 1-4.
    • Handle: RePEc:eee:stapro:v:112:y:2016:i:c:p:1-4
    DOI: 10.1016/j.spl.2015.12.028
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    References listed on IDEAS

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    1. Janet E. Heffernan & Jonathan A. Tawn, 2004. "A conditional approach for multivariate extreme values (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 497-546, August.
    2. Papastathopoulos, Ioannis & Strokorb, Kirstin, 2016. "Conditional independence among max-stable laws," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 9-15.
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