Conditional limiting distribution of Type III elliptical random vectors

  • Authors:

  • Enkelejd Hashorva

  • Affiliations:

  • Allianz Suisse Insurance Company, Laupenstrasse 27, CH-3001 Bern, Switzerland and Department of Statistics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2007

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Abstract

In this paper we consider elliptical random vectors in R^d,d=2 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 R^d and A@?R^d^x^d 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 R^d. Further, we derive an asymptotic approximation for the conditional distribution of such random vectors.