IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v201y2023ics0167715223001098.html
   My bibliography  Save this article

Nonsymmetric examples for Gaussian correlation inequalities

Author

Listed:
  • Huang, Chien-Hao

Abstract

In this paper, we compare two variances of maxima of N standard Gaussian random variables. One is a sequence of N i.i.d. standard Gaussians, and the other one is N standard Gaussians with covariances σ1,2=ρ∈(0,1) and σi,j=0, for other i≠j. It turns out that we need to discuss the covariance of two functions with respect to multivariate Gaussian distributions. Gaussian correlation inequalities hold for many symmetric (with respect to the origin) cases. However, in our case, the max function and its derivatives are not symmetric about the origin. We have two main results in this paper. First, we prove a specific case for a convex/log-concave correlation inequality for the standard multivariate Gaussian distribution. The other result is that the variance of maxima of standard Gaussians with σ1,2=ρ∈(0,1), while σi,j=0, for other i≠j, is larger than the variance of maxima of independent standard Gaussians. This implies that the variance of maxima of N i.i.d. standard Gaussians is decreasing in N.

Suggested Citation

  • Huang, Chien-Hao, 2023. "Nonsymmetric examples for Gaussian correlation inequalities," Statistics & Probability Letters, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:stapro:v:201:y:2023:i:c:s0167715223001098
    DOI: 10.1016/j.spl.2023.109885
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715223001098
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2023.109885?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    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:stapro:v:201:y:2023:i:c:s0167715223001098. 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/622892/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.