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Limit distribution of the sum and maximum from multivariate Gaussian sequences


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  • James, Barry
  • James, Kang
  • Qi, Yongcheng
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    In this paper we study the asymptotic joint behavior of the maximum and the partial sum of a multivariate Gaussian sequence. The multivariate maximum is defined to be the coordinatewise maximum. Results extend univariate results of McCormick and Qi. We show that, under regularity conditions, if the maximum has a limiting distribution it is asymptotically independent of the partial sum. We also prove that the maximum of a stationary sequence, when normalized in a special sense which includes subtracting the sample mean, is asymptotically independent of the partial sum (again, under regularity conditions). The limiting distributions are also obtained.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 3 (March)
    Pages: 517-532

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:517-532

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    Keywords: Gaussian process Maximum Sum Stationary sequence;


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    1. Wisniewski, Mateusz, 1996. "On extreme-order statistics and point processes of exceedances in multivariate stationary Gaussian sequences," Statistics & Probability Letters, Elsevier, vol. 29(1), pages 55-59, August.
    2. Hüsler, Jürg & Schüpbach, Michel, 1988. "Limit results for maxima in non-stationary multivariate Gaussian sequences," Stochastic Processes and their Applications, Elsevier, vol. 28(1), pages 91-99, April.
    3. Amram, Fred, 1985. "Multivariate extreme value distributions for stationary Gaussian sequences," Journal of Multivariate Analysis, Elsevier, vol. 16(2), pages 237-240, April.
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    Cited by:
    1. Aiping Hu & Zuoxiang Peng & Yongcheng Qi, 2009. "Joint behavior of point process of exceedances and partial sum from a Gaussian sequence," Metrika, Springer, vol. 70(3), pages 279-295, November.
    2. Peng, Zuoxiang & Cao, Lunfeng & Nadarajah, Saralees, 2010. "Asymptotic distributions of maxima of complete and incomplete samples from multivariate stationary Gaussian sequences," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2641-2647, November.


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