IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v26y2017i2d10.1007_s11749-016-0516-0.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-016-0516-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-016-0516-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    3. 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.
    4. 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.
    5. 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.
    6. Chris Hans, 2009. "Bayesian lasso regression," Biometrika, Biometrika Trust, vol. 96(4), pages 835-845.
    7. 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.
    8. 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.
    9. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(4), pages 230-354, June.
    2. Paul Hofmarcher & Jesús Crespo Cuaresma & Bettina Grün & Kurt Hornik, 2015. "Last Night a Shrinkage Saved My Life: Economic Growth, Model Uncertainty and Correlated Regressors," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(2), pages 133-144, March.
    3. 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.
    4. Jesus Crespo Cuaresma & Bettina Grün & Paul Hofmarcher & Stefan Humer & Mathias Moser, 2015. "A Comprehensive Approach to Posterior Jointness Analysis in Bayesian Model Averaging Applications," Department of Economics Working Papers wuwp193, Vienna University of Economics and Business, Department of Economics.
    5. Aart Kraay & Norikazu Tawara, 2013. "Can specific policy indicators identify reform priorities?," Journal of Economic Growth, Springer, vol. 18(3), pages 253-283, September.
    6. Crespo Cuaresma, Jesus & von Schweinitz, Gregor & Wendt, Katharina, 2019. "On the empirics of reserve requirements and economic growth," Journal of Macroeconomics, Elsevier, vol. 60(C), pages 253-274.
    7. Bruns, Stephan B. & Ioannidis, John P.A., 2020. "Determinants of economic growth: Different time different answer?," Journal of Macroeconomics, Elsevier, vol. 63(C).
    8. 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.
    9. Korobilis, Dimitris, 2013. "Hierarchical shrinkage priors for dynamic regressions with many predictors," International Journal of Forecasting, Elsevier, vol. 29(1), pages 43-59.
    10. Rockey, James & Temple, Jonathan, 2016. "Growth econometrics for agnostics and true believers," European Economic Review, Elsevier, vol. 81(C), pages 86-102.
    11. Ruggieri, Eric & Lawrence, Charles E., 2012. "On efficient calculations for Bayesian variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1319-1332.
    12. Kourtellos, Andros & Marr, Christa & Tan, Chih Ming, 2016. "Robust determinants of intergenerational mobility in the land of opportunity," European Economic Review, Elsevier, vol. 81(C), pages 132-147.
    13. Hofmarcher, Paul & Crespo Cuaresma, Jesus & Grün, Bettina & Humer, Stefan & Moser, Mathias, 2018. "Bivariate jointness measures in Bayesian Model Averaging: Solving the conundrum," Journal of Macroeconomics, Elsevier, vol. 57(C), pages 150-165.
    14. Posch, Konstantin & Arbeiter, Maximilian & Pilz, Juergen, 2020. "A novel Bayesian approach for variable selection in linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    15. Fouskakis, Dimitris & Ntzoufras, Ioannis & Perrakis, Konstantinos, 2020. "Variations of power-expected-posterior priors in normal regression models," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    16. P. Richard Hahn & Carlos M. Carvalho, 2015. "Decoupling Shrinkage and Selection in Bayesian Linear Models: A Posterior Summary Perspective," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 435-448, March.
    17. Havranek, Tomas & Horvath, Roman & Irsova, Zuzana & Rusnak, Marek, 2015. "Cross-country heterogeneity in intertemporal substitution," Journal of International Economics, Elsevier, vol. 96(1), pages 100-118.
    18. Dimitris Korobilis, 2018. "Machine Learning Macroeconometrics: A Primer," Working Paper series 18-30, Rimini Centre for Economic Analysis.
    19. Baragatti, M. & Pommeret, D., 2012. "A study of variable selection using g-prior distribution with ridge parameter," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1920-1934.
    20. Salimans, Tim, 2012. "Variable selection and functional form uncertainty in cross-country growth regressions," Journal of Econometrics, Elsevier, vol. 171(2), pages 267-280.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:26:y:2017:i:2:d:10.1007_s11749-016-0516-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.