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On the number of points near the multivariate maxima

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  • Hashorva, Enkelejd
  • Hüsler, Jürg
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    Abstract

    Let {Xi, i[greater-or-equal, slanted]1} be a sequence of independent random vectors with common continuous distribution function F. In this paper, we consider the number of the elements from X1,...,Xn which fall in some random region determined by the maximum. Both distributional and asymptotic results are obtained.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-44B58C8-9/2/b5d8ca673d4e0aab60bedf3b530dae8d
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 55 (2001)
    Issue (Month): 2 (November)
    Pages: 113-124

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    Handle: RePEc:eee:stapro:v:55:y:2001:i:2:p:113-124

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    Related research

    Keywords: Max-stable distributions Point processes Weak convergence Almost sure convergence;

    References

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    1. Khmaladze, E. & Nadareishvili, M. & Nikabadze, A., 1997. "Asymptotic behaviour of a number of repeated records," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 49-58, August.
    2. Li, Yun, 1999. "A note on the number of records near the maximum," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 153-158, June.
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    Cited by:
    1. Bairamov, I. & Stepanov, A., 2011. "Numbers of near bivariate record-concomitant observations," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 908-917, May.
    2. Bairamov, I. & Stepanov, A., 2010. "Numbers of near-maxima for the bivariate case," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 196-205, February.
    3. Hashorva, Enkelejd, 2004. "Bivariate maximum insurance claim and related point processes," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 117-128, August.

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