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Asymptotics of the norm of elliptical random vectors

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  • Hashorva, Enkelejd

Abstract

In this paper we consider elliptical random vectors in with stochastic representation , where R is a positive random radius independent of the random vector which is uniformly distributed on the unit sphere of and is a given matrix. Denote by ||[dot operator]|| the Euclidean norm in , and let F be the distribution function of R. The main result of this paper is an asymptotic expansion of the probability for F in the Gumbel or the Weibull max-domain of attraction. In the special case that is a mean zero Gaussian random vector our result coincides with the one derived in Hüsler et al. (2002) [1].

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  • Hashorva, Enkelejd, 2010. "Asymptotics of the norm of elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 926-935, April.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:4:p:926-935
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    References listed on IDEAS

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    1. Berman, Simeon M., 1983. "Sojourns and extremes of Fourier sums and series with random coefficients," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 213-238, August.
    2. Drees, Burkhard, 1992. "Financial institutions or asset markets: Alternative trading and banking arrangements as risk sharing mechanisms," European Journal of Political Economy, Elsevier, vol. 8(2), pages 175-200, May.
    3. 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.
    4. Hashorva, Enkelejd, 2007. "Conditional limiting distribution of Type III elliptical random vectors," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 282-294, February.
    5. Hüsler, Jürg & Liu, Regina Y. & Singh, Kesar, 2002. "A Formula for the Tail Probability of a Multivariate Normal Distribution and Its Applications," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 422-430, August.
    6. Hashorva, Enkelejd, 2006. "On the regular variation of elliptical random vectors," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1427-1434, August.
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    Cited by:

    1. Nadarajah, Saralees, 2015. "Complete asymptotic expansions for normal extremes," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 127-133.
    2. Hashorva, Enkelejd, 2015. "Extremes of aggregated Dirichlet risks," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 334-345.
    3. Hashorva, Enkelejd & Pakes, Anthony G. & Tang, Qihe, 2010. "Asymptotics of random contractions," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 405-414, December.

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