IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v36y1991i2p199-203.html
   My bibliography  Save this article

Association and infinite divisibility for the Wishart distribution and its diagonal marginals

Author

Listed:
  • Evans, Steven N.

Abstract

We give an example of a central Wishart matrix W with one degree of freedom and scale matrix of rank 2 such that the diagonal entries of W are not associated. This allows us to conclude that no central Wishart matrix with one degree of freedom and scale matrix of rank greater than 1 is associated. We also employ the connection between association and infinite divisibility to show that, despite former evidence to the contrary, there exist Gaussian vectors such that the vector of squares is not infinitely divisible. Similarly, we obtain another proof of Lévy's result that no central Wishart matrix with scale matrix of rank greater than 1 is infinitely divisible.

Suggested Citation

  • Evans, Steven N., 1991. "Association and infinite divisibility for the Wishart distribution and its diagonal marginals," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 199-203, February.
    • Handle: RePEc:eee:jmvana:v:36:y:1991:i:2:p:199-203
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(91)90057-9
    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. Kozubowski, Tomasz J. & Mazur, Stepan & Podgórski, Krzysztof, 2022. "Matrix Gamma Distributions and Related Stochastic Processes," Working Papers 2022:12, Örebro University, School of Business.
    2. Finner, Helmut & Roters, Markus, 2024. "On positive association of absolute-valued and squared multivariate Gaussians beyond MTP2," Journal of Multivariate Analysis, Elsevier, vol. 202(C).

    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:jmvana:v:36:y:1991:i:2:p:199-203. 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.