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Extremes of conditioned elliptical random vectors

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  • Hashorva, Enkelejd

Abstract

Let {Xn,n[greater-or-equal, slanted]1} be iid elliptical random vectors in and let I,J be two non-empty disjoint index sets. Denote by Xn,I,Xn,J the subvectors of Xn with indices in I,J, respectively. For any such that aJ is in the support of X1,J the conditional random sample Xn,IXn,J=aJ,n>=1 consists of elliptically distributed random vectors. In this paper we investigate the relation between the asymptotic behaviour of the multivariate extremes of the conditional sample and the unconditional one. We show that the asymptotic behaviour of the multivariate extremes of both samples is the same, provided that the associated random radius of X1 has distribution function in the max-domain of attraction of a univariate extreme value distribution.

Suggested Citation

  • Hashorva, Enkelejd, 2007. "Extremes of conditioned elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1583-1591, September.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:8:p:1583-1591
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    References listed on IDEAS

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    1. Berman, Simeon M., 1983. "Sojourns and extremes of Fourier sums and series with random coefficients," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 213-238, August.
    2. Hashorva, Enkelejd, 2005. "Extremes of asymptotically spherical and elliptical random vectors," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 285-302, June.
    3. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
    4. Kotz, S. & Ostrovskii, I., 1994. "Characteristic Functions of a Class of Elliptic Distributions," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 164-178, April.
    5. Hashorva, Enkelejd, 2006. "On the regular variation of elliptical random vectors," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1427-1434, August.
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