IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v121y2011i3p515-533.html
   My bibliography  Save this article

Extremes of the standardized Gaussian noise

Author

Listed:
  • Kabluchko, Zakhar

Abstract

Let be a d-dimensional array of independent standard Gaussian random variables. For a finite set define . Let A be the number of elements in A. We prove that the appropriately normalized maximum of , where A ranges over all discrete cubes or rectangles contained in {1,...,n}d, converges in law to the Gumbel extreme-value distribution as n-->[infinity]. We also prove a continuous-time counterpart of this result.

Suggested Citation

  • Kabluchko, Zakhar, 2011. "Extremes of the standardized Gaussian noise," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 515-533, March.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:3:p:515-533
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(10)00265-6
    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.

    Citations

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


    Cited by:

    1. Kabluchko, Zakhar & Wang, Yizao, 2014. "Limiting distribution for the maximal standardized increment of a random walk," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2824-2867.
    2. Hotz, Thomas & Marnitz, Philipp & Stichtenoth, Rahel & Davies, Laurie & Kabluchko, Zakhar & Munk, Axel, 2012. "Locally adaptive image denoising by a statistical multiresolution criterion," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 543-558.
    3. Guenther Walther & Andrew Perry, 2022. "Calibrating the scan statistic: Finite sample performance versus asymptotics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1608-1639, November.
    4. Zhongquan Tan & Shengchao Zheng, 2020. "Extremes of a Type of Locally Stationary Gaussian Random Fields with Applications to Shepp Statistics," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2258-2279, December.

    Corrections

    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:spapps:v:121:y:2011:i:3:p:515-533. See general information about how to correct material in RePEc.

    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.

    We have no bibliographic references for this item. You can help adding them by using 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.