IDEAS home Printed from
   My bibliography  Save this article

Limit distribution of the sum and maximum from multivariate Gaussian sequences


  • James, Barry
  • James, Kang
  • Qi, Yongcheng


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.

Suggested Citation

  • James, Barry & James, Kang & Qi, Yongcheng, 2007. "Limit distribution of the sum and maximum from multivariate Gaussian sequences," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 517-532, March.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:517-532

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Amram, Fred, 1985. "Multivariate extreme value distributions for stationary Gaussian sequences," Journal of Multivariate Analysis, Elsevier, vol. 16(2), pages 237-240, April.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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: International Journal for Theoretical and Applied Statistics, 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.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:98:y:2007:i:3:p:517-532. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.