A Revision of AIC for Normal Error Models

Kunio Takezawa

Agroinformatics Division, National Agricultural Research Center Graduate School of Life and Environmental Sciences, University of Tsukuba, Tsukuba, Japan.

DOI: 10.4236/ojs.2012.23038                

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.

Keywords

AIC; AIC_c; Normal Error Models; Third Variance

Conflicts of Interest

The authors declare no conflicts of interest.

References

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