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A Revision of <i>AIC</i> for Normal Error Models

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Author(s): Kunio Takezawa

Journal: Open Journal of Statistics
ISSN 2161-718X

Volume: 02;
Issue: 03;
Start page: 309;
Date: 2012;
Original page

Keywords: AIC | AICc | Normal Error Models | Third Variance

ABSTRACT
Conventional Akaike’s Information Criterion (AIC) for normal error models uses the maximum-likelihood estimator of error variance. Other estimators of error variance, however, can be employed for defining AIC for normal error models. The maximization of the log-likelihood using an adjustable error variance in light of future data yields a revised version of AIC for normal error models. It also gives a new estimator of error variance, which will be called the “third variance”. If the model is described as a constant plus normal error, which is equivalent to fitting a normal distribution to one-dimensional data, the approximated value of the third variance is obtained by replacing (n-1) (n is the number of data) of the unbiased estimator of error variance with (n-4). The existence of the third variance is confirmed by a simple numerical simulation.
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