IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i6p547-554.html
   My bibliography  Save this article

Minimax estimation of a bounded parameter of a discrete distribution

Author

Listed:
  • Marchand, Éric
  • Parsian, Ahmad

Abstract

For a vast class of discrete model families with cdf's F[theta], and for estimating [theta] under squared error loss under a constraint of the type [theta][set membership, variant][0,m], we present a general and unified development concerning the minimaxity of a boundary supported prior Bayes estimator. While the sufficient conditions obtained are of the expected form m[less-than-or-equals, slant]m(F), the approach presented leads, in many instances, to both necessary and sufficient conditions, and/or explicit values for m(F). Finally, the scope of the results is illustrated with various examples that, not only include several common distributions (e.g., Poisson, Binomial, Negative Binomial), but many others as well.

Suggested Citation

  • Marchand, Éric & Parsian, Ahmad, 2006. "Minimax estimation of a bounded parameter of a discrete distribution," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 547-554, March.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:6:p:547-554
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00344-5
    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. Marchand Éric & MacGibbon Brenda, 2000. "Minimax Estimation Of A Constrained Binomial Proportion," Statistics & Risk Modeling, De Gruyter, vol. 18(2), pages 129-168, February.
    Full references (including those not matched with items on IDEAS)

    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. Mohammad Jozani & Éric Marchand, 2007. "Minimax estimation of constrained parametric functions for discrete families of distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(2), pages 151-160, September.
    2. Wojciech Gamrot, 2013. "Maximum likelihood estimation for ordered expectations of correlated binary variables," Statistical Papers, Springer, vol. 54(3), pages 727-739, August.

    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:76:y:2006:i:6:p:547-554. 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.