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

An assumption for the development of bootstrap variants of the Akaike information criterion in mixed models

Listed author(s):
  • Shang, Junfeng
  • Cavanaugh, Joseph E.
Registered author(s):

    This note provides a proof of a fundamental assumption in the verification of bootstrap AIC variants in mixed models. The assumption links the bootstrap data and the original sample data via the log-likelihood function, and is the key condition used in the validation of the criterion penalty terms. (See Assumption 3 of both Shibata [Shibata, R., 1997. Bootstrap estimate of Kullback-Leibler information for model selection. Statistica Sinica 7, 375-394] and Shang and Cavanaugh [Shang, J., Cavanaugh, J.E., 2008. Bootstrap variants of the Akaike information criterion for mixed model selection. Computational Statistics and Data Analysis 52, 2004-2021]. To state the assumption, let Y and Y* represent the response vector and the corresponding bootstrap sample, respectively. Let [theta] represent the set of parameters for a candidate mixed model, and let denote the corresponding maximum likelihood estimator based on maximizing the likelihood L([theta]|Y). With E* denoting the expectation with respect to the bootstrap distribution of Y*, the assumption asserts that . We prove that the assumption holds under parametric, semiparametric, and nonparametric bootstrapping.

    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 Statistics & Probability Letters.

    Volume (Year): 78 (2008)
    Issue (Month): 12 (September)
    Pages: 1422-1429

    in new window

    Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1422-1429
    Contact details of provider: Web page:

    Order Information: Postal:

    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. Shang, Junfeng & Cavanaugh, Joseph E., 2008. "Bootstrap variants of the Akaike information criterion for mixed model selection," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2004-2021, January.
    2. Morris, Jeffrey S., 2002. "The BLUPs are not "best" when it comes to bootstrapping," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 425-430, February.
    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:eee:stapro:v:78:y:2008:i:12:p:1422-1429. 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.