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Biometrika 1996 83(4):875-890; doi:10.1093/biomet/83.4.875
© 1996 by Biometrika Trust
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Generalised information criteria in model selection

SADANORI KONISHI and GENSHIRO KITAGAWA

Graduate School of Mathematics, Kyushu University 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812, Japan
The Institute of Statistical Mathematics 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106, Japan

The problem of evaluating the goodness of statistical models is investigated from an information-theoretic point of view. Information criteria are proposed for evaluating models constructed by various estimation procedures when the specified family of probability distributions does not contain the distribution generating the data. The proposed criteria are applied to the evaluation of models estimated by maximum likelihood, robust, penalised likelihood, Bayes procedures, etc. We also discuss the use of the bootstrap in model evaluation problems and present a variance reduction technique in the bootstrap simulation.

Key Words: AIC • Bayes approach • Efficient bootstrap simulation • Information criterion • M-estimators • Penalised likelihood • Predictive distribution • Statistical functional


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