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Multiple maxima in multivariate samples

Author

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  • Hashorva, Enkelejd
  • Hüsler, Jürg

Abstract

Let {Xn,n[greater-or-equal, slanted]1} be a sequence of independent random vectors in , with common continuous distribution function F. For fixed n[greater-or-equal, slanted]2, we say that a multiple maximum occurs among the sample points X1,...,Xn if Mn=Xi for some i=1,...,n, with Mn the componentwise sample maximum. In this paper, we investigate the asymptotic behaviour (n-->[infinity]) of the probability of observing a multiple maximum by imposing an asymptotic tail condition on F.

Suggested Citation

  • Hashorva, Enkelejd & Hüsler, Jürg, 2005. "Multiple maxima in multivariate samples," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 11-17, November.
    • Handle: RePEc:eee:stapro:v:75:y:2005:i:1:p:11-17
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    References listed on IDEAS

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    1. Gnedin, Alexander V., 1998. "Records from a multivariate normal sample," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 11-15, July.
    2. Enkelejd Hashorva & Jürg Hüsler, 2003. "On multivariate Gaussian tails," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 507-522, September.
    3. Gnedin, A. V., 1993. "On Multivariate Extremal Processes," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 207-213, August.
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    Cited by:

    1. Stoev, Stilian & Wang, Yizao, 2019. "Exchangeable random partitions from max-infinitely-divisible distributions," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 50-56.
    2. Ismihan Bayramoglu, 2016. "On the records of multivariate random sequences," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(6), pages 725-747, August.
    3. Hashorva Enkelejd, 2016. "Domination of sample maxima and related extremal dependence measures," Dependence Modeling, De Gruyter, vol. 6(1), pages 88-101, May.
    4. Hashorva, Enkelejd & Rullière, Didier, 2020. "Asymptotic domination of sample maxima," Statistics & Probability Letters, Elsevier, vol. 160(C).
    5. Clément Dombry & Michael Falk & Maximilian Zott, 2019. "On Functional Records and Champions," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1252-1277, September.

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