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Elliptical triangular arrays in the max-domain of attraction of Hüsler-Reiss distribution

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  • Hashorva, Enkelejd

Abstract

Let be a triangular array of independent bivariate elliptical random vectors. Hüsler and Reiss (1989. Statist. Probab. Lett. 7, 283-286) show that for the particular case that the array is Gaussian, the maxima of this array is in the max-domain of attraction of Hüsler-Reiss distribution function, provided that an asymptotic condition holds for the correlation corr(Un1,Vn1). In this paper we obtain a similar result for the more general case of elliptical triangular arrays.

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  • 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.
    • Handle: RePEc:eee:stapro:v:72:y:2005:i:2:p:125-135
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    1. 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.
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    Cited by:

    1. Hashorva, Enkelejd & Weng, Zhichao, 2013. "Limit laws for extremes of dependent stationary Gaussian arrays," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 320-330.
    2. Hashorva, Enkelejd, 2006. "A novel class of bivariate max-stable distributions," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1047-1055, May.
    3. Opitz, T., 2013. "Extremal t processes: Elliptical domain of attraction and a spectral representation," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 409-413.
    4. Hashorva, Enkelejd, 2005. "Extremes of asymptotically spherical and elliptical random vectors," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 285-302, June.
    5. 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.
    6. Enkelejd Hashorva & Zuoxiang Peng & Zhichao Weng, 2016. "Higher-order expansions of distributions of maxima in a Hüsler-Reiss model," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 181-196, March.
    7. Frick, Melanie & Reiss, Rolf-Dieter, 2010. "Limiting distributions of maxima under triangular schemes," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2346-2357, November.
    8. Hashorva, Enkelejd, 2008. "Tail asymptotic results for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 158-164, August.
    9. Frick, Melanie & Reiss, Rolf-Dieter, 2013. "Expansions and penultimate distributions of maxima of bivariate normal random vectors," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2563-2568.
    10. 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.
    11. 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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