Modified AIC and Cp in multivariate linear regression

The Akaike information criterion, AIC, and the Mallows' C p criterion have been proposed as approximately unbiased estimators for their risks or underlying criterion functions. In this paper we propose modified AIC and C P , for selecting multivariate linear regression models. Our modified AIC and modified C p are intended to reduce bias in situations where the collection of candidate models includes both underspecified and overspecified models. In a simulation study it is verified that the modified AIC and modified C p provide better approximations to their risk functions, and better model selection, than AIC and C p .