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AN APPLICATION OF MULTIPLE COMPARISON

TECHNIQUES TO MODEL SELECTION

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HIDETOSHI SIMODAIRA

*Department of Mathematical Engineering and Information Physics,*

University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan
(Received April 15, 1996; revised March 26, 1997)

**Abstract.**
Akaike's information criterion
(AIC) is widely used to estimate the best model from a
given candidate set of parameterized probabilistic
models. In this paper, considering the sampling error
of AIC, a set of good models is constructed rather
than choosing a single model. This set is called a
confidence set of models, which includes the minimum
\cal E{AIC} model at an error rate smaller than
the specified significance level. The result is given
as *P*-value for each model, from which the confidence
set is immediately obtained. A variant of Gupta's
subset selection procedure is devised, in which a
standardized difference of AIC is calculated for every
pair of models. The critical constants are computed by
the Monte-Carlo method, where the asymptotic normal
approximation of AIC is used. The proposed method
neither requires the full model nor assumes a
hierarchical structure of models, and it has higher
power than similar existing methods.

*Key words and phrases*:
Akaike's
information criterion, model selection, confidence
set, multiple comparison with the best, Gupta's subset
selection, variable selection, multiple regression,
bootstrap resampling.

**Source**
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