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

A third-order optimum property of the maximum likelihood estimator

Listed author(s):
  • Pfanzagl, J.
  • Wefelmeyer, W.
Registered author(s):

    Let [theta](n) denote the maximum likelihood estimator of a vector parameter, based on an i.i.d. sample of size n. The class of estimators [theta](n) + n-1 q([theta](n)), with q running through a class of sufficiently smooth functions, is essentially complete in the following sense: For any estimator T(n) there exists q such that the risk of [theta](n) + n-1 q([theta](n)) exceeds the risk of T(n) by an amount of order o(n-1) at most, simultaneously for all loss functions which are bounded, symmetric, and neg-unimodal. If q* is chosen such that [theta](n) + n-1 q*([theta](n)) is unbiased up to o(n-1/2), then this estimator minimizes the risk up to an amount of order o(n-1) in the class of all estimators which are unbiased up to o(n-1/2). The results are obtained under the assumption that T(n) admits a stochastic expansion, and that either the distributions have--roughly speaking--densities with respect to the lebesgue measure, or the loss functions are sufficiently smooth.

    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: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 8 (1978)
    Issue (Month): 1 (March)
    Pages: 1-29

    in new window

    Handle: RePEc:eee:jmvana:v:8:y:1978:i:1:p:1-29
    Contact details of provider: Web page:

    Order Information: Postal:

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

    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:eee:jmvana:v:8:y:1978:i:1:p:1-29. 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: (Dana Niculescu)

    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.