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Maxima of a triangular array of multivariate Gaussian sequence

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  • Hashorva, Enkelejd
  • Peng, Liang
  • Weng, Zhichao

Abstract

It is known that the normalized maxima of a sequence of independent and identically distributed bivariate normal random vectors with correlation coefficient ρ∈[−1,1) is asymptotically independent, which implies that using bivariate normal distribution will seriously underestimate extreme co-movement in practice. By letting ρ depend on the sample size and go to one with certain rate, Hüsler and Reiss (1989) showed that the normalized maxima of Gaussian random vectors can become asymptotically dependent so as to well predict the co-movement observed in the market. In this paper, we extend such a study to a triangular array of a multivariate Gaussian sequence, which further generalizes the results in Hsing et al. (1996) and Hashorva and Weng (2013).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:103:y:2015:i:c:p:62-72
    DOI: 10.1016/j.spl.2015.04.007
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Hashorva, Enkelejd & Weng, Zhichao, 2013. "Limit laws for extremes of dependent stationary Gaussian arrays," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 320-330.
    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. Jinhui Guo & Yingyin Lu, 2023. "Joint behavior of point processes of clusters and partial sums for stationary bivariate Gaussian triangular arrays," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(1), pages 17-37, February.

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