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A note on the unification of the Akaike information criterion

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  • P. Shi
  • C‐L. Tsai

Abstract

To measure the distance between a robust function evaluated under the true regression model and under a fitted model, we propose generalized Kullback–Leibler information. Using this generalization we have developed three robust model selection criteria, AICR*, AICCR* and AICCR, that allow the selection of candidate models that not only fit the majority of the data but also take into account non‐normally distributed errors. The AICR* and AICCR criteria can unify most existing Akaike information criteria; three examples of such unification are given. Simulation studies are presented to illustrate the relative performance of each criterion.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:3:p:551-558
    DOI: 10.1111/1467-9868.00139
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    Cited by:

    1. Liping Zhu & Rui Shi & Lincheng Mi & Pu Liu & Guofeng Wang, 2022. "Spatial Distribution and Convergence of Agricultural Green Total Factor Productivity in China," IJERPH, MDPI, vol. 19(14), pages 1-16, July.
    2. Gorobets, A., 2004. "The Optimal Prediction Simultaneous Equations Selection," ERIM Report Series Research in Management ERS-2003-023-ORG, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. La Vecchia, Davide & Camponovo, Lorenzo & Ferrari, Davide, 2015. "Robust heart rate variability analysis by generalized entropy minimization," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 137-151.
    4. Giuzio, Margherita & Ferrari, Davide & Paterlini, Sandra, 2016. "Sparse and robust normal and t- portfolios by penalized Lq-likelihood minimization," European Journal of Operational Research, Elsevier, vol. 250(1), pages 251-261.
    5. Kenneth Burnham & Gary White, 2002. "Evaluation of some random effects methodology applicable to bird ringing data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(1-4), pages 245-264.
    6. Čížek, Pavel, 2004. "(Non) Linear Regression Modeling," Papers 2004,11, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).

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