Conditional limiting distribution of Type III elliptical random vectors

Enkelejd Hashorva

Journal of Multivariate Analysis, 2007, vol. 98, issue 2, 282-294

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.

Keywords: Asymptotic; approximation; Elliptical; random; vectors; Conditional; distribution; Weibull; max-domain; of; attraction; Weak; convergence (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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