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A Note on AIC and TIC for Model Selection

Author

Listed:
  • Yong Li

    (Renmin University of China)

  • Zhou Wu

    (Zhejiang University)

  • Jun Yu

    (University of Macau)

  • Tao Zeng

    (Zhejiang University)

Abstract

This note gives a rigorous justification to Akaike information criterion (AIC) and Takeuchi information criterion (TIC). The existing literature has shown that, when the candidate model is a good approximation of the true data generating process (DGP), AIC is an asymptotic unbiased estimator of the expected Kullback-Leibler divergence between the DGP and the plug-in predictive distribution. When the candidate model is misspecified, TIC can be regraded as a robust version of AIC with its justification following a similar line of argument. However, the justifications in current literature are predominantly confined to the iid scenario. In this note, we establish the asymptotic unbiasedness of AIC and TIC under certain regular conditions. These conditions are applicable in various scenarios, encompassing weakly dependent data.

Suggested Citation

  • Yong Li & Zhou Wu & Jun Yu & Tao Zeng, 2024. "A Note on AIC and TIC for Model Selection," Working Papers 202420, University of Macau, Faculty of Business Administration.
    • Handle: RePEc:boa:wpaper:202420
    as

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    File URL: https://fba.um.edu.mo/wp-content/uploads/RePEc/doc/202420.pdf
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    References listed on IDEAS

    as
    1. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, January.
    2. 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.
    3. P. Shi & C‐L. Tsai, 1998. "A note on the unification of the Akaike information criterion," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 551-558.
    4. Li, Yong & Yu, Jun & Zeng, Tao, 2020. "Deviance information criterion for latent variable models and misspecified models," Journal of Econometrics, Elsevier, vol. 216(2), pages 450-493.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    AIC; TIC; Expected loss function; Kullback-Leibler divergence; Model selection; Plug-in predictive distribution; weakly dependent data.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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