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Asymptotic domination of sample maxima

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  • Hashorva, Enkelejd
  • Rullière, Didier

Abstract

For a given random sample from some underlying multivariate distribution F we consider the domination of the component-wise maxima by some independent random vector W with distribution function G. We show that the probability that certain components of the sample maxima are dominated by the corresponding components of W can be approximated under the assumptions that both F and G are in the max-domain of attraction of some max-stable distribution functions. We study further some basic probabilistic properties of the dominated components of sample maxima by W.

Suggested Citation

  • Hashorva, Enkelejd & Rullière, Didier, 2020. "Asymptotic domination of sample maxima," Statistics & Probability Letters, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:stapro:v:160:y:2020:i:c:s0167715220300067
    DOI: 10.1016/j.spl.2020.108703
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    1. Genest, Christian & Rivest, Louis-Paul, 1989. "A characterization of gumbel's family of extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 207-211, August.
    2. Hashorva, Enkelejd & Hüsler, Jürg, 2005. "Multiple maxima in multivariate samples," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 11-17, November.
    3. Stoev, Stilian & Wang, Yizao, 2019. "Exchangeable random partitions from max-infinitely-divisible distributions," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 50-56.
    4. Clément Dombry & Mathieu Ribatet & Stilian Stoev, 2018. "Probabilities of Concurrent Extremes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1565-1582, October.
    5. Gnedin, Alexander V., 1998. "Records from a multivariate normal sample," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 11-15, July.
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