Second-order bias-corrected AIC in multivariate normal linear models under non-normality

作者：Yanagihara Hirokazu^*; Kamo Ken Ichi; Tonda Tetsuji

来源：Canadian Journal of Statistics, 2011, 39(1): 126-146.

DOI：10.1002/cjs.10090

• Akaike's information criterion
• bias correction
• Kullback-Leibler information
• model misspecification
• normal assumption
• overspecified model
• selection of variables
• predicted residual sum of squares
• robustness to non-normality
• variance of information criterion

This paper deals with a bias correction of Akaike's information criterion (AIC) for selecting variables in multivariate normal linear regression models when the true distribution of observation is an unknown non-normal distribution. It is well known that the bias of AIC is O(1), and there are a number of the first-order bias-corrected AICs which improve the bias to O(n(-1)), where n is the sample size. A new information criterion is proposed by slightly adjusting the first-order bias-corrected AIC. Although the adjustment is achieved by merely using constant coefficients, the bias of the new criterion is reduced to O(n(-2)). Then, a variance of the new criterion is also improved. Through numerical experiments, we verify that our criterion is superior to others.

• 出版日期2011-3