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On the multivariate Hüsler-Reiss distribution attracting the maxima of elliptical triangular arrays

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  • Hashorva, Enkelejd

Abstract

Let , be a triangular array of independent elliptical random vectors in . In this paper we investigate the asymptotic behaviour of the multivariate maxima of this triangular array. Generalising previous results for the bivariate set-up, we show that the normalised maxima of this elliptical triangular array is attracted by the multivariate Hüsler-Reiss distribution function provided that the components of the triangular array become asymptotically dependent with a specific rate, and further the random radius pertaining to the elliptical random vectors is in the Gumbel max-domain of attraction.

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  • Hashorva, Enkelejd, 2006. "On the multivariate Hüsler-Reiss distribution attracting the maxima of elliptical triangular arrays," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 2027-2035, December.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:18:p:2027-2035
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    References listed on IDEAS

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    1. Hashorva, Enkelejd, 2005. "Extremes of asymptotically spherical and elliptical random vectors," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 285-302, June.
    2. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
    3. Kotz, Samuel & Nadarajah, Saralees, 2001. "Some extremal type elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 171-182, September.
    4. Hashorva, Enkelejd, 2005. "Elliptical triangular arrays in the max-domain of attraction of Hüsler-Reiss distribution," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 125-135, April.
    5. Hüsler, Jürg & Reiss, Rolf-Dieter, 1989. "Maxima of normal random vectors: Between independence and complete dependence," Statistics & Probability Letters, Elsevier, vol. 7(4), pages 283-286, February.
    6. 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.
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    Cited by:

    1. Hashorva, Enkelejd, 2008. "Conditional limiting distribution of beta-independent random vectors," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1438-1459, August.
    2. Hashorva, Enkelejd, 2009. "Asymptotics for Kotz Type III elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 927-935, April.
    3. Manjunath, B.G. & Frick, Melanie & Reiss, Rolf-Dieter, 2012. "Some notes on extremal discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 107-115, January.
    4. Weng, Zhichao & Liao, Xin, 2017. "Second order expansions of distributions of maxima of bivariate Gaussian triangular arrays under power normalization," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 33-43.

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