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Expansions and penultimate distributions of maxima of bivariate normal random vectors

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  • Frick, Melanie
  • Reiss, Rolf-Dieter

Abstract

It is well known that the marginal maxima of n standard normal random vectors with correlation coefficient ρ<1 are asymptotically independent. In this article, the residual dependence will be captured by asymptotic expansions and certain penultimate distributions including the case where ρ(n)↑1 at a certain rate.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:11:p:2563-2568
    DOI: 10.1016/j.spl.2013.08.004
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    References listed on IDEAS

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    1. Padoan, Simone A., 2011. "Multivariate extreme models based on underlying skew-t and skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 977-991, May.
    2. 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.
    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. 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).
    2. 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.
    3. Hashorva, Enkelejd & Peng, Liang & Weng, Zhichao, 2015. "Maxima of a triangular array of multivariate Gaussian sequence," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 62-72.
    4. Wang, Rui & Liao, Xin & Peng, Zuoxiang, 2017. "Second-order expansions for maxima of dynamic bivariate normal copulas," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 275-283.

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