IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v92y2005i2p454-464.html
   My bibliography  Save this article

The admissibility of the empirical mean location for the matrix von Mises-Fisher family

Author

Listed:
  • Hendriks, Harrie

Abstract

In this note we consider von Mises-Fisher families of probability densities on spheres and more generally on Stiefel manifolds, which include the orthogonal groups. It addresses the estimation of the mean direction or the mean location by empirical mean location, which for the von Mises-Fisher family coincides with the maximum likelihood estimator. It is shown that (with a few exceptions) the empirical mean location of a sample is almost surely uniquely defined and that it is unbiased in the sense that its mean location coincides with the mean location of the von Mises-Fisher distribution. The main goal, however, is to show that empirical mean location is an admissible estimator for the mean location of the von Mises-Fisher distribution.

Suggested Citation

  • Hendriks, Harrie, 2005. "The admissibility of the empirical mean location for the matrix von Mises-Fisher family," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 454-464, February.
    • Handle: RePEc:eee:jmvana:v:92:y:2005:i:2:p:454-464
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00215-X
    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

    as
    1. Hendriks, Harrie, 1991. "A Cramér-Rao type lower bound for estimators with values in a manifold," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 245-261, August.
    2. Kim, Peter T., 1991. "Decision theoretic analysis of spherical regression," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 233-240, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Kanika, & Kumar, Somesh & SenGupta, Ashis, 2015. "A unified approach to decision-theoretic properties of the MLEs for the mean directions of several Langevin distributions," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 160-172.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Oualkacha, Karim & Rivest, Louis-Paul, 2009. "A new statistical model for random unit vectors," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 70-80, January.
    2. Steven E. Pav, 2014. "Bounds on Portfolio Quality," Papers 1409.5936, arXiv.org.
    3. Hendriks, Harrie & Landsman, Zinoviy, 1996. "Asymptotic behavior of sample mean location for manifolds," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 169-178, February.

    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:92:y:2005:i:2:p:454-464. 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.

    If CitEc recognized a bibliographic 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.

    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.