IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v70y2004i1p87-94.html
   My bibliography  Save this article

Shrinkage estimation for convex polyhedral cones

Author

Listed:
  • Amirdjanova, Anna
  • Woodroofe, Michael

Abstract

Estimation of a multivariate normal mean is considered when the latter is known to belong to a convex polyhedron. It is shown that shrinking the maximum likelihood estimator towards an appropriate target can reduce mean squared error. The proof combines an unbiased estimator of a risk difference with some geometrical considerations. When applied to the monotone regression problem, the main result shows that shrinking the maximum likelihood estimator towards modifications that have been suggested to alleviate the spiking problem can reduce mean squared error.

Suggested Citation

  • Amirdjanova, Anna & Woodroofe, Michael, 2004. "Shrinkage estimation for convex polyhedral cones," Statistics & Probability Letters, Elsevier, vol. 70(1), pages 87-94, October.
  • Handle: RePEc:eee:stapro:v:70:y:2004:i:1:p:87-94
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(04)00230-5
    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. Ouassou, Idir & Strawderman, William E., 2002. "Estimation of a parameter vector restricted to a cone," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 121-129, January.
    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. Tsukuma Hisayuki, 2009. "Shrinkage estimation in elliptically contoured distribution with restricted parameter space," Statistics & Risk Modeling, De Gruyter, vol. 27(1), pages 25-35, November.

    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. Hisayuki Tsukuma, 2012. "Simultaneous estimation of restricted location parameters based on permutation and sign-change," Statistical Papers, Springer, vol. 53(4), pages 915-934, November.
    2. Tsukuma Hisayuki, 2009. "Shrinkage estimation in elliptically contoured distribution with restricted parameter space," Statistics & Risk Modeling, De Gruyter, vol. 27(1), pages 25-35, November.
    3. Fourdrinier, Dominique & Ouassou, Idir & Strawderman, William E., 2003. "Estimation of a parameter vector when some components are restricted," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 14-27, July.
    4. Dominique Fourdrinier & William Strawderman & Martin Wells, 2006. "Estimation of a Location Parameter with Restrictions or “vague information” for Spherically Symmetric Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(1), pages 73-92, March.
    5. Chang, Yuan-Tsung & Matsuda, Takeru & Strawderman, William E., 2019. "A note on improving on a vector of coordinate-wise estimators of non-negative means via shrinkage," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 143-150.

    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:70:y:2004:i:1:p:87-94. 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.