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

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. The Canadian Journal of Statistics 39: 126–146; 2011 © 2011 Statistical Society of Canada