Asymptotics of the norm of elliptical random vectors

  • Authors:

  • Enkelejd Hashorva

  • Affiliations:

  • Department of Statistics, University of Bern, Sidlerstrasse 5, CH-3012, Bern, Switzerland

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2010

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Abstract

In this paper we consider elliptical random vectors X in R^d,d=2 with stochastic representation ARU, 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 given matrix. Denote by @?@?@? the Euclidean norm in R^d, and let F be the distribution function of R. The main result of this paper is an asymptotic expansion of the probability P{@?X@?u} for F in the Gumbel or the Weibull max-domain of attraction. In the special case that X is a mean zero Gaussian random vector our result coincides with the one derived in Husler et al. (2002) [1].