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.
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.