A Revision of AIC for Normal Error Models

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.