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 (C) 2011 Statistical Society of Canada