A Revision of <i>AIC</i>for Normal Error Models

• 作者: Kunio Takezawa
• 来源期刊: 统计学期刊(英文)
• 学科: 数学
• 关键词: AIC AICc NORMAL Error Models THIRD Variance
• 年，卷（期）: 2012,（3）
• 页码范围: 309-312
• 页数: 4页
• 分类号: O1

摘要

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.