Abstract
During the last fifteen years, Akaike's Information Criteria (IC) 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. Asumptotic 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.