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Conditional limiting distribution of Type III elliptical random vectors

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  • Hashorva, Enkelejd

Abstract

In this paper we consider elliptical random vectors in with stochastic representation RAU where R is a positive random radius independent of the random vector U which is uniformly distributed on the unit sphere of and is a non-singular matrix. When R has distribution function in the Weibull max-domain of attraction we say that the corresponding elliptical random vector is of Type III. For the bivariate set-up, Berman [Sojurns and Extremes of Stochastic Processes, Wadsworth & Brooks/ Cole, 1992] obtained for Type III elliptical random vectors an interesting asymptotic approximation by conditioning on one component. In this paper we extend Berman's result to Type III elliptical random vectors in . Further, we derive an asymptotic approximation for the conditional distribution of such random vectors.

Suggested Citation

  • Hashorva, Enkelejd, 2007. "Conditional limiting distribution of Type III elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 282-294, February.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:2:p:282-294
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    References listed on IDEAS

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    1. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    2. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
    3. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
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    Cited by:

    1. Hashorva, Enkelejd, 2010. "Asymptotics of the norm of elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 926-935, April.
    2. Hashorva, Enkelejd, 2008. "Conditional limiting distribution of beta-independent random vectors," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1438-1459, August.

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