Advanced Search
MyIDEAS: Login

On the minimax regret estimation of a restricted normal mean, and implications

Contents:

Author Info

  • Droge, Bernd
Registered author(s):

    Abstract

    Consider estimating the mean of a normal distribution with known variance, when that mean is known to lie in a bounded interval. In a decision-theoretic framework we study finite sample properties of a class of nonlinear' estimators. These estimators are based on thresholding techniques which have become very popular in the context of wavelet estimation. Under squared errorloss we show that there exists unique minimax regret solution for the problem of selecting the threshold. For comparison, the behaviour' of linear shrinkers is also investigated. In special cases we illustrate the implications of our results for the problem of estimating the regression function in a nonparametric situation. This is possible since, as usual, a, coordinatewise application of the scalar results leads immediately to results for multivariate (sequence space) problems. Then it is well known that orthogonal transformations can be employed to turn statements about estimation over coefficient bodies in sequence space into statements about estimation over classes of smooth functions in noisy data. The performance of the proposed minimax regret optimal curve estimator is demonstrated by simulated data examples. --

    Download Info

    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: http://econstor.eu/bitstream/10419/65311/1/727077163.pdf
    Download Restriction: no

    Bibliographic Info

    Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2002,81.

    as in new window
    Length:
    Date of creation: 2002
    Date of revision:
    Handle: RePEc:zbw:sfb373:200281

    Contact details of provider:
    Postal: Spandauer Str. 1,10178 Berlin
    Phone: +49-30-2093-5708
    Fax: +49-30-2093-5617
    Email:
    Web page: http://www.wiwi.hu-berlin.de/
    More information through EDIRC

    Related research

    Keywords: Bounded normal mean; soft thresholding; minimax regret decision theory; non linear estirnation; nonparametric regression; orthogonal series estimation;

    References

    No references listed on IDEAS
    You can help add them by filling out this form.

    Citations

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

    Cited by:
    1. Droge, Bernd, 2006. "Minimax regret comparison of hard and soft thresholding for estimating a bounded normal mean," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 83-92, January.

    Lists

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

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:zbw:sfb373:200281. 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: (ZBW - German National Library of Economics).

    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.