IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v15y1984i1p21-51.html
   My bibliography  Save this article

Two testing problems relating the real and complex multivariate normal distributions

Author

Listed:
  • Andersson, Steen A.
  • Perlman, Michael D.

Abstract

The first problem considered is that of testing for the reality of the covariance matrix of a p-dimensional complex normal distribution, while the second is that of testing that a 2p-dimensional real normal distribution has a p-dimensional complex structure. Both problems are reduced by invariance to their maximal invariant statistics, and the null and non-null distributions of these are obtained. Complete classes of unbiased, invariant tests are described for both problems, the locally most powerful invariant tests are obtained, and the admissibility of the likelihood ratio tests is established.

Suggested Citation

  • Andersson, Steen A. & Perlman, Michael D., 1984. "Two testing problems relating the real and complex multivariate normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 15(1), pages 21-51, August.
    • Handle: RePEc:eee:jmvana:v:15:y:1984:i:1:p:21-51
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(84)90065-4
    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. Konno, Yoshihiko, 2007. "Estimation of normal covariance matrices parametrized by irreducible symmetric cones under Stein's loss," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 295-316, February.
    2. Norbert Henze & Pierre Lafaye De Micheaux & Simos G. Meintanis, 2022. "Tests for circular symmetry of complex-valued random vectors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 488-518, June.

    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:15:y:1984:i:1:p:21-51. 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.