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A mixture of g-priors for variable selection when the number of regressors grows with the sample size

Author

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  • Minerva Mukhopadhyay

    (Indian Statistical Institute)

  • Tapas Samanta

    (Indian Statistical Institute)

Abstract

We consider the problem of variable selection in linear regression using mixtures of g-priors. A number of mixtures have been proposed in the literature which work well, especially when the number of regressors p is fixed. In this paper, we propose a mixture of g-priors suitable for the case when p grows with the sample size n, more specifically when $$p=O(n^b)$$ p = O ( n b ) , $$0

Suggested Citation

  • Minerva Mukhopadhyay & Tapas Samanta, 2017. "A mixture of g-priors for variable selection when the number of regressors grows with the sample size," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 377-404, June.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:2:d:10.1007_s11749-016-0516-0
    DOI: 10.1007/s11749-016-0516-0
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    References listed on IDEAS

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    1. Jinchi Lv & Jun S. Liu, 2014. "Model selection principles in misspecified models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 141-167, January.
    2. Ley, Eduardo & Steel, Mark F.J., 2012. "Mixtures of g-priors for Bayesian model averaging with economic applications," Journal of Econometrics, Elsevier, vol. 171(2), pages 251-266.
    3. Chris Hans, 2009. "Bayesian lasso regression," Biometrika, Biometrika Trust, vol. 96(4), pages 835-845.
    4. Howard D. Bondell & Brian J. Reich, 2012. "Consistent High-Dimensional Bayesian Variable Selection via Penalized Credible Regions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1610-1624, December.
    5. M. J. Bayarri & G. García‐Donato, 2008. "Generalization of Jeffreys divergence‐based priors for Bayesian hypothesis testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 981-1003, November.
    6. 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.
    7. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    8. 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.
    9. Valen E. Johnson & David Rossell, 2012. "Bayesian Model Selection in High-Dimensional Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 649-660, June.
    10. Minerva Mukhopadhyay & Tapas Samanta & Arijit Chakrabarti, 2015. "On consistency and optimality of Bayesian variable selection based on $$g$$ g -prior in normal linear regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 963-997, October.
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    Cited by:

    1. Mark F. J. Steel, 2020. "Model Averaging and Its Use in Economics," Journal of Economic Literature, American Economic Association, vol. 58(3), pages 644-719, September.

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