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A Revision of AIC for Normal Error Models

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DOI: 10.4236/ojs.2012.23038    4,600 Downloads   9,404 Views Citations
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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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K. Takezawa, "A Revision of AIC for Normal Error Models," Open Journal of Statistics, Vol. 2 No. 3, 2012, pp. 309-312. doi: 10.4236/ojs.2012.23038.

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