, Volume 52, Issue 3, pp 345-370

Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions

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Abstract

During the last fifteen years, Akaike's entropy-based Information Criterion (AIC) has had a fundamental impact in statistical model evaluation problems. This paper studies the general theory of the AIC procedure and provides its analytical extensions in two ways without violating Akaike's main principles. These extensions make AIC asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the “true” models. These selection criteria are called CAIC and CAICF. Asymptotic properties of AIC and its extensions are investigated, and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different Monte Carlo experiments under different conditions.

The author extends his deep appreciation to many people. These include Hirotugu Akaike, Donald E. Ramirez, Marvin Rosenblum, and S. James Taylor for reading and commenting on some parts of this manuscript through various stages of its development. I especially wish to thank Yoshio Takane, Jim Ramsay, and Stanley L. Sclove for critically reading the paper and making many helpful suggestions. I also wish to thank Julie Riddleberger for her excellent typing of this manuscript.
This research was partially supported by NIH Biomedical Research Support Grant (BRSG) No. 5-24867 at the University of Virginia.