Model Selection and Akaike's Information Criterion (AIC): The General Theory and its Analytical Extensions

Bozdogan, Hamparsum

doi:10.1007/bf02294361

Cited by 4,468Statistical Methods and InferenceStatistical Methods and ApplicationsStatistical Methods and Bayesian Inference

Model Selection and Akaike's Information Criterion (AIC): The General Theory and its Analytical Extensions

Bozdogan, Hamparsum·1987·Psychometrika

DOI 10.1007/bf02294361

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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.

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AIC introduces a penalty for the number of parameters in the model, which increases with the number of Gaussian components and dimensions of the data.
“AIC introduces a penalty for the number of parameters in the model (which increases with the number of Gaussian components and dimensions of the data).”
From Improving Environment Novelty Quantification for Effective Unsupervised Environment Design (2024) · cites this paper as [15]
ALP-GMM evaluates the GMM's quality using Akaike's Information Criterion (AIC).
“However, they evaluate the GMM's quality using the Akaike's Information Criterion [15] (AIC).”
From Improving Environment Novelty Quantification for Effective Unsupervised Environment Design (2024) · cites this paper as [15]

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Authors: Bozdogan, H.
Affiliations: University of Virginia (US)
Corresponding author: Bozdogan, Hamparsum
ORCID: Bozdogan, Hamparsum
Venue: Psychometrika
Publisher: Cambridge University Press (CUP)
Published: 1987-09
Volume: 52
Issue: 3
Pages: 345-370
ISSN: 0033-3123 (ISSN-L)
1860-0980
DOI: 10.1007/bf02294361
OpenAlex: W1981903823
Cited by: 4,468
References: 5
Citations by year: 2026: 157 · 2025: 255 · 2024: 273 · 2023: 290 · 2022: 271 · 2021: 282 · 2020: 269 · 2019: 237 · 2018: 243 · 2017: 206 · 2016: 197 · 2015: 180 · 2014: 161 · 2013: 157 · 2012: 117
FWCI: 12.44
Type: journal article
Language: en
Open access: closed
Licence: www.cambridge.org/core/terms (unspecified, 13637 d)
Locations: Psychometrika (publishedVersion)
RePEc: Research Papers in Economics (submittedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Keywords: Akaike information criterion, model selection, CAIC, asymptotic consistency, model evaluation

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Model Selection and Akaike's Information Criterion (AIC): The General Theory and its Analytical Extensions

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