An assumption for the development of bootstrap variants of the Akaike information criterion in mixed models
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.
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.
Volume (Year): 78 (2008)
Issue (Month): 12 (September)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
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.:
- 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.
- 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.
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: (Zhang, Lei)
If references are entirely missing, you can add them using this form.