Journal article
An assumption for the development of bootstrap variants of the Akaike information criterion in mixed models
Statistics & probability letters, Vol.78(12), pp.1422-1429
2008
DOI: 10.1016/j.spl.2007.12.015
Abstract
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
θ
represent the set of parameters for a candidate mixed model, and let
θ
ˆ
denote the corresponding maximum likelihood estimator based on maximizing the likelihood
L
(
θ
∣
Y
)
. With
E
∗
denoting the expectation with respect to the bootstrap distribution of
Y
∗
, the assumption asserts that
E
∗
log
L
(
θ
ˆ
∣
Y
∗
)
=
log
L
(
θ
ˆ
∣
Y
)
. We prove that the assumption holds under parametric, semiparametric, and nonparametric bootstrapping.
Details
- Title: Subtitle
- An assumption for the development of bootstrap variants of the Akaike information criterion in mixed models
- Creators
- Junfeng Shang - Bowling Green State University, USAJoseph E Cavanaugh - The University of Iowa, USA
- Resource Type
- Journal article
- Publication Details
- Statistics & probability letters, Vol.78(12), pp.1422-1429
- DOI
- 10.1016/j.spl.2007.12.015
- ISSN
- 0167-7152
- eISSN
- 1879-2103
- Publisher
- Elsevier B.V
- Language
- English
- Date published
- 2008
- Academic Unit
- Statistics and Actuarial Science; Biostatistics; Injury Prevention Research Center
- Record Identifier
- 9984214700102771
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