IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v58y2002i4p327-333.html
   My bibliography  Save this article

On the minimax estimator of a bounded normal mean

Author

Listed:
  • Marchand, Éric
  • Perron, François

Abstract

For estimating under squared-error loss the mean of a p-variate normal distribution when this mean lies in a ball of radius m centered at the origin and the covariance matrix is equal to the identity matrix, it is shown that the Bayes estimator with respect to a uniformly distributed prior on the boundary of the parameter space ([delta]BU) is minimax whenever . Further descriptions of the cutoff points of small enough radiuses (i.e., m[less-than-or-equals, slant]m0(p)) for [delta]BU to be minimax are given. These include lower bounds and the large dimension p limiting behaviour of . Finally, implications for the associated minimax risk are described.

Suggested Citation

  • Marchand, Éric & Perron, François, 2002. "On the minimax estimator of a bounded normal mean," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 327-333, July.
    • Handle: RePEc:eee:stapro:v:58:y:2002:i:4:p:327-333
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(02)00089-5
    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. Robert, Christian, 1990. "Modified Bessel functions and their applications in probability and statistics," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 155-161, February.
    2. Berry, J. Calvin, 1990. "Minimax estimation of a bounded normal mean vector," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 130-139, October.
    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. Marchand, Éric & Perron, François, 2005. "Improving on the mle of a bounded location parameter for spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 227-238, February.
    2. Éric Marchand & François Perron, 2009. "Estimating a bounded parameter for symmetric distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 215-234, March.
    3. Fourdrinier, Dominique & Marchand, Éric, 2010. "On Bayes estimators with uniform priors on spheres and their comparative performance with maximum likelihood estimators for estimating bounded multivariate normal means," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1390-1399, July.

    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. Fourdrinier, Dominique & Marchand, Éric, 2010. "On Bayes estimators with uniform priors on spheres and their comparative performance with maximum likelihood estimators for estimating bounded multivariate normal means," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1390-1399, July.
    2. Andrés Martín & Ernesto Estrada, 2023. "Fractional-Modified Bessel Function of the First Kind of Integer Order," Mathematics, MDPI, vol. 11(7), pages 1-13, March.
    3. Marchand, Éric & Perron, François, 2005. "Improving on the mle of a bounded location parameter for spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 227-238, February.
    4. Marchand Éric & MacGibbon Brenda, 2000. "Minimax Estimation Of A Constrained Binomial Proportion," Statistics & Risk Modeling, De Gruyter, vol. 18(2), pages 129-168, February.
    5. Árpád Baricz & Dragana Jankov Maširević & Tibor K. Pogány, 2021. "Approximation of CDF of Non-Central Chi-Square Distribution by Mean-Value Theorems for Integrals," Mathematics, MDPI, vol. 9(2), pages 1-12, January.
    6. Jan Beran & Britta Steffens & Sucharita Ghosh, 2022. "On nonparametric regression for bivariate circular long-memory time series," Statistical Papers, Springer, vol. 63(1), pages 29-52, February.
    7. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2008. "Stein's phenomenon in estimation of means restricted to a polyhedral convex cone," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 141-164, January.
    8. Éric Marchand & François Perron, 2009. "Estimating a bounded parameter for symmetric distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 215-234, March.

    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:58:y:2002:i:4:p:327-333. 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.