Model Selection and Akaike's Information Criterion (AIC): The General Theory and its Analytical Extensions
1987/09/01 by Hamparsum Bozdogan · 4,551 citations
Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Akaike information criterion #Applied mathematics #Artificial intelligence #Bayesian information criterion #Computer science #Econometrics #Entropy (arrow of time) #Information Criteria #Information theory #Mathematics #Model selection #Monte Carlo method #Selection (genetic algorithm) #Statistical Mechanics and Entropy #Statistical Methods and Inference #Statistics
paper · doi:10.1007/bf02294361
published in Psychometrika 52(3), 345-370 (Springer Science+Business Media)
openalex publication_date 1987/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.
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