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Regularization in Regression : Comparing Bayesian and Frequentist Methods in a Poorly Informative Situation

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  • Gilles Celeux

    (Crest)

  • Mohammed El Anbari

    (Crest)

  • Jean-Michel Marin

    (Crest)

  • Christian P. Robert

    (Crest)

Abstract

We propose a global noninformative approach for Bayesian variable selection that builds onZellner’s g-priors and is similar to Liang et al. (2008). Our proposal does not require any kindof calibration. In the case of a benchmark, we compare Bayesian and frequentist regularizationapproaches under a low informative constraint when the number of variables is almost equalto the number of observations. The simulated and real dataset experiments we present herehighlight the appeal of Bayesian regularization methods, when compared with alternatives.They dominate frequentist methods in the sense they provide smaller prediction errors whileselecting the most relevant variables in a parsimonious way.

Suggested Citation

  • Gilles Celeux & Mohammed El Anbari & Jean-Michel Marin & Christian P. Robert, 2010. "Regularization in Regression : Comparing Bayesian and Frequentist Methods in a Poorly Informative Situation," Working Papers 2010-43, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2010-43
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Philips, R. & Guttman, I., 1998. "A new criterion for variable selection," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 11-19, May.
    3. P. J. Brown & M. Vannucci & T. Fearn, 1998. "Multivariate Bayesian variable selection and prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 627-641.
    4. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    5. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    6. Casella, George & Moreno, Elias, 2006. "Objective Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 157-167, March.
    7. repec:dau:papers:123456789/1906 is not listed on IDEAS
    8. repec:dau:papers:123456789/857 is not listed on IDEAS
    9. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    10. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    11. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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