A Revision of AIC for Normal Error Models


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.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] K. P. Burnham and D. R. Anderson, “Model Selection and Multi-Model Inference A Practical Information- Theoretic Approach,” Springer, Berlin, 2010.
[2] S. Konishi and G. Kitagawa, “Information Criteria and Statistical Modeling,” Springer, Berlin, 2007.
[3] C. M. Hurvich and C.-L. Tsai, “Regression and Time Series Model Selection in Small Samples,” Biometrika, Vol. 76, No. 2, 1989, pp. 297-307. doi:10.1093/biomet/76.2.297
[4] N. Sugiura, “Further Analysis of the Data by Akaike’s Information Criterion and Finite Corrections,” Communications in Statistics-Theory and Methods, Vol. 7, No. 1, 1978, pp. 13-26. doi:10.1080/03610927808827599

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