IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Minimaxity in Predictive Density Estimation with Parametric Constraints

Listed author(s):
  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

  • Éric Marchand

    (Département de mathématiques, Université de Sherbrooke,)

  • William E. Strawderman

    (Department of Statistics and Biostatistics, Rutgers University,)

  • Jean-Philippe Turcotte

    (Département de mathématiques, Université de Sherbrooke,)

Registered author(s):

    This paper is concerned with estimation of a predictive density with parametric constraints under Kullback-Leibler loss. When an invariance structure is embed- ded in the problem, general and uni ed conditions for the minimaxity of the best equivariant predictive density estimator are derived. These conditions are applied to check minimaxity in various restricted parameter spaces in location and/or scale families. Further, it is shown that the generalized Bayes estimator against the uni- form prior over the restricted space is minimax and dominates the best equivariant estimator in a location family when the parameter is restricted to an interval of the form [a0;1). Similar ndings are obtained for scale parameter families. Finally, the presentation is accompanied by various observations and illustrations, such as normal, exponential location, and gamma model examples.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Download Restriction: no

    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-843.

    in new window

    Length: 27 pages
    Date of creation: Feb 2012
    Handle: RePEc:tky:fseres:2012cf843
    Contact details of provider: Postal:
    Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033

    Phone: +81-3-5841-5644
    Fax: +81-3-5841-8294
    Web page:

    More information through EDIRC

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    in new window

    1. José Manuel Corcuera, 1999. "A Generalized Bayes Rule for Prediction," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 265-279.
    2. Éric Marchand & William Strawderman, 2005. "Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 129-143, March.
    3. Kengo Kato, 2009. "Improved prediction for a multivariate normal distribution with unknown mean and variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 531-542, September.
    4. Hartigan, J. A., 2004. "Uniform priors on convex sets improve risk," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 285-288, May.
    5. Tatsuya Kubokawa, 2004. "Minimaxity in Estimation of Restricted Parameters," CIRJE F-Series CIRJE-F-270, CIRJE, Faculty of Economics, University of Tokyo.
    6. Tatsuya Kubokawa, 1994. "Double shrinkage estimation of ratio of scale parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 95-116, March.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:tky:fseres:2012cf843. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CIRJE administrative office)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.