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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   9,405 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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

References

[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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