# 赤池信息量准则

## AIC

${\displaystyle AIC=2k-2\ln(L)\,}$

${\displaystyle AIC=2k+n\ln(RSS/n)\,}$

## AICc和AICu

${\displaystyle AICc=AIC+{\frac {2k(k+1)}{n-k-1}}\,}$

n增加时，AICc收敛成AIC。所以AICc可以应用在任何样本大小的情况下（Burnham and Anderson, 2004）。

McQuarrie 和 Tsai（1998: 22）把AICc定义为：

${\displaystyle AICc=\ln {\frac {RSS}{n}}+{\frac {n+k}{n-k-2}}\ ,}$

${\displaystyle AICu=\ln {\frac {RSS}{n-k}}+{\frac {n+k}{n-k-2}}\ .}$

## QAIC

QAIC（Quasi-AIC）可以定义为：

${\displaystyle QAIC=2k-{\frac {1}{c}}2\ln {L}\,}$

${\displaystyle QAICc=QAIC+{\frac {2k(k+1)}{n-k-1}}\,}$.

## 参考文献

• Akaike, Hirotsugu. A new look at the statistical model identification. IEEE Transactions on Automatic Control. 1974, 19 (6): 716–723.
• Burnham, K. P., and D. R. Anderson, 2002. Model Selection and Multimodel Inference: A Practical-Theoretic Approach, 2nd ed. Springer-Verlag. ISBN 0-387-95364-7.
• --------, 2004. Multimodel Inference: understanding AIC and BIC in Model Selection页面存档备份，存于互联网档案馆, Amsterdam Workshop on Model Selection.
• Hurvich, C. M., and Tsai, C.-L., 1989. Regression and time series model selection in small samples. Biometrika, Vol 76. pp. 297-307
• McQuarrie, A. D. R., and Tsai, C.-L., 1998. Regression and Time Series Model Selection. World Scientific.