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A large-sample model selection criterion based on Kullback's symmetric divergence

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  • Cavanaugh, Joseph E.

Abstract

The Akaike information criterion, AIC, is a widely known and extensively used tool for statistical model selection. AIC serves as an asymptotically unbiased estimator of a variant of Kullback's directed divergence between the true model and a fitted approximating model. The directed divergence is an asymmetric measure of separation between two statistical models, meaning that an alternate directed divergence may be obtained by reversing the roles of the two models in the definition of the measure. The sum of the two directed divergences is Kullback's symmetric divergence. Since the symmetric divergence combines the information in two related though distinct measures, it functions as a gauge of model disparity which is arguably more sensitive than either of its individual components. With this motivation, we propose a model selection criterion which serves as an asymptotically unbiased estimator of a variant of the symmetric divergence between the true model and a fitted approximating model. We examine the performance of the criterion relative to other well-known criteria in a simulation study.

Suggested Citation

  • Cavanaugh, Joseph E., 1999. "A large-sample model selection criterion based on Kullback's symmetric divergence," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 333-343, May.
  • Handle: RePEc:eee:stapro:v:42:y:1999:i:4:p:333-343
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    References listed on IDEAS

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    1. 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.
    2. Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 243-247, December.
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    Cited by:

    1. Kim, Jae-Young, 2014. "An alternative quasi likelihood approach, Bayesian analysis and data-based inference for model specification," Journal of Econometrics, Elsevier, vol. 178(P1), pages 132-145.
    2. Nicolas Depraetere & Martina Vandebroek, 2014. "Order selection in finite mixtures of linear regressions," Statistical Papers, Springer, vol. 55(3), pages 871-911, August.
    3. Hafidi, Bezza, 2006. "A small-sample criterion based on Kullback's symmetric divergence for vector autoregressive modeling," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1647-1654, September.
    4. Hafidi, Bezza & Mkhadri, Abdallah, 2010. "The Kullback information criterion for mixture regression models," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 807-815, May.
    5. repec:spr:compst:v:33:y:2018:i:2:d:10.1007_s00180-017-0766-7 is not listed on IDEAS
    6. Hafidi, B. & Mkhadri, A., 2006. "A corrected Akaike criterion based on Kullback's symmetric divergence: applications in time series, multiple and multivariate regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1524-1550, March.
    7. Kim, Jae-Young, 2012. "Model selection in the presence of nonstationarity," Journal of Econometrics, Elsevier, vol. 169(2), pages 247-257.
    8. Daniel F. Schmidt & Enes Makalic, 2013. "Estimation of stationary autoregressive models with the Bayesian LASSO," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 517-531, September.
    9. Christopher H. Jackson & Simon G. Thompson & Linda D. Sharples, 2009. "Accounting for uncertainty in health economic decision models by using model averaging," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(2), pages 383-404, April.
    10. Marhuenda, Yolanda & Morales, Domingo & del Carmen Pardo, María, 2014. "Information criteria for Fay–Herriot model selection," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 268-280.

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