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Unifying the derivations for the Akaike and corrected Akaike information criteria

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  • Cavanaugh, Joseph E.

Abstract

The Akaike (1973, 1974) information criterion, AIC, and the corrected Akaike information criterion (Hurvich and Tsai, 1989), AICc, were both designed as estimators of the expected Kullback-Leibler discrepancy between the model generating the data and a fitted candidate model. AIC is justified in a very general framework, and as a result, offers a crude estimator of the expected discrepancy: one which exhibits a potentially high degree of negative bias in small-sample applications (Hurvich and Tsai, 1989). AICc corrects for this bias, but is less broadly applicable than AIC since its justification depends upon the form of the candidate model (Hurvich and Tsai, 1989, 1993; Hurvich et al., 1990; Bedrick and Tsai, 1994). Although AIC and AICc share the same objective, the derivations of the criteria proceed along very different lines, making it difficult to reconcile how AICc improves upon the approximations leading to AIC. To address this issue, we present a derivation which unifies the justifications of AIC and AICc in the linear regression framework.

Suggested Citation

  • Cavanaugh, Joseph E., 1997. "Unifying the derivations for the Akaike and corrected Akaike information criteria," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 201-208, April.
    • Handle: RePEc:eee:stapro:v:33:y:1997:i:2:p:201-208
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    References listed on IDEAS

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    1. J. M. Bernardo, 1976. "Psi (Digamma) Function," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(3), pages 315-317, November.
    2. Clifford M. Hurvich & Chih‐Ling Tsai, 1993. "A Corrected Akaike Information Criterion For Vector Autoregressive Model Selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 271-279, May.
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