# 赤池信息量准则

## AIC

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

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

## AICc和AICu

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

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：

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

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

## QAIC

QAIC（Quasi-AIC）可以定义为：

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

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

## 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, 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.