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An Akaike-type information criterion for model selection under inequality constraints

Author

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  • R. M. Kuiper
  • H. Hoijtink
  • M. J. Silvapulle

Abstract

The Akaike information criterion for model selection presupposes that the parameter space is not subject to order restrictions or inequality constraints. Anraku (1999) proposed a modified version of this criterion, called the order-restricted information criterion, for model selection in the one-way analysis of variance model when the population means are monotonic. We propose a generalization of this to the case when the population means may be restricted by a mixture of linear equality and inequality constraints. If the model has no inequality constraints, then the generalized order-restricted information criterion coincides with the Akaike information criterion. Thus, the former extends the applicability of the latter to model selection in multi-way analysis of variance models when some models may have inequality constraints while others may not. Simulation shows that the information criterion proposed in this paper performs well in selecting the correct model. Copyright 2011, Oxford University Press.

Suggested Citation

  • R. M. Kuiper & H. Hoijtink & M. J. Silvapulle, 2011. "An Akaike-type information criterion for model selection under inequality constraints," Biometrika, Biometrika Trust, vol. 98(2), pages 495-501.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:2:p:495-501
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    File URL: http://hdl.handle.net/10.1093/biomet/asr002
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    Cited by:

    1. Oh, Man-Suk, 2014. "Bayesian comparison of models with inequality and equality constraints," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 176-182.
    2. Kuiper, Rebecca M. & Hoijtink, Herbert, 2013. "A Fortran 90 Program for the Generalized Order-Restricted Information Criterion," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i08).
    3. Pietro Coretto, 2022. "Estimation and computations for Gaussian mixtures with uniform noise under separation constraints," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 427-458, June.

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