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Higher-order expansions of distributions of maxima in a Hüsler-Reiss model

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  • Enkelejd Hashorva

    (University of Lausanne)

  • Zuoxiang Peng

    (Southwest University)

  • Zhichao Weng

    (University of Lausanne)

Abstract

The max-stable Hüsler-Reiss distribution which arises as the limit distribution of maxima of bivariate Gaussian triangular arrays has been shown to be useful in various extreme value models. For such triangular arrays, this paper establishes higher-order asymptotic expansions of the joint distribution of maxima under refined Hüsler-Reiss conditions. In particular, the rate of convergence of normalized maxima to the Hüsler-Reiss distribution is explicitly calculated. Our findings are supported by the results of a numerical analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:1:d:10.1007_s11009-014-9407-6
    DOI: 10.1007/s11009-014-9407-6
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    References listed on IDEAS

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    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. Engelke, S. & Kabluchko, Z. & Schlather, M., 2011. "An equivalent representation of the Brown-Resnick process," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1150-1154, August.
    3. 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.
    4. Hooghiemstra, G. & Hüsler, J., 1996. "A note on maxima of bivariate random vectors," Statistics & Probability Letters, Elsevier, vol. 31(1), pages 1-6, December.
    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.
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    Cited by:

    1. Hu, Shuang & Peng, Zuoxiang & Nadarajah, Saralees, 2022. "Tail dependence functions of the bivariate Hüsler–Reiss model," Statistics & Probability Letters, Elsevier, vol. 180(C).

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