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Biometrika 1997 84(3):707-716; doi:10.1093/biomet/84.3.707
© 1997 by Biometrika Trust
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Modified AIC and Cp in multivariate linear regression

YASUNORI FUJIKOSHI and KENICHI SATOH

Department of Mathematics, Faculty of Science, Hiroshima University 1-3-1 Kagamiyama, Higashihiroshima-City, 739 Japan e-mail: fuji{at}math.sci.hiroshima-u.ac.jp ksatoh{at}ipc.hiroshima-u.ac.jp

The Akaike information criterion, AIC, and the Mallows' Cp criterion have been proposed as approximately unbiased estimators for their risks or underlying criterion functions. In this paper we propose modified AIC and Cp, for selecting multivariate linear regression models. Our modified AIC and modified Cp 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 Cp provide better approximations to their risk functions, and better model selection, than AIC and Cp.

Key Words: Akaike information criterion • Bias properties • Mallows' Cp criterion • Modified AIC • Modified Cp • Multivariate linear regression • Selection of variables


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