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Asymptotic Domination of Sample Maxima

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  • Enkelejd Hashorva

    (UNIL - Université de Lausanne = University of Lausanne)

  • Didier Rullière

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

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 underlying 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 function F and G, respectively. We study further some basic properties of the dominated components of sample maxima by W .

Suggested Citation

  • Enkelejd Hashorva & Didier Rullière, 2020. "Asymptotic Domination of Sample Maxima," Post-Print hal-02277020, HAL.
    • Handle: RePEc:hal:journl:hal-02277020
    DOI: 10.1016/j.spl.2020.108703
    Note: View the original document on HAL open archive server: https://hal.science/hal-02277020
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    References listed on IDEAS

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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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