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Conditional limiting distribution of Type III elliptical random vectors


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  • Hashorva, Enkelejd
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    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.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 2 (February)
    Pages: 282-294

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:2:p:282-294

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    Keywords: Asymptotic approximation Elliptical random vectors Conditional distribution Weibull max-domain of attraction Weak convergence;


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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.


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