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Bayesian Semiparametric Regression

Author

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  • Pelenis, Justinas

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria)

Abstract

We consider Bayesian estimation of restricted conditional moment models with linear regression as a particular example. The standard practice in the Bayesian literature for semiparametric models is to use flexible families of distributions for the errors and assume that the errors are independent from covariates. However, a model with flexible covariate dependent error distributions should be preferred for the following reasons: consistent estimation of the parameters of interest even if errors and covariates are dependent; possibly superior prediction intervals and more efficient estimation of the parameters under heteroscedasticity. To address these issues, we develop a Bayesian semiparametric model with flexible predictor dependent error densities and with mean restricted by a conditional moment condition. Sufficient conditions to achieve posterior consistency of the regression parameters and conditional error densities are provided. In experiments, the proposed method compares favorably with classical and alternative Bayesian estimation methods for the estimation of the regression coefficients.

Suggested Citation

  • Pelenis, Justinas, 2012. "Bayesian Semiparametric Regression," Economics Series 285, Institute for Advanced Studies.
  • Handle: RePEc:ihs:ihsesp:285
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    File URL: http://www.ihs.ac.at/publications/eco/es-285.pdf
    File Function: First version, 2012
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    References listed on IDEAS

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    1. Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
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    5. Amisano, Gianni & Geweke, John, 2007. "Hierarchical Markov normal mixture models with applications to financial asset returns," Working Paper Series 831, European Central Bank.
    6. Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
    7. Norets, Andriy & Pelenis, Justinas, 2014. "Posterior Consistency In Conditional Density Estimation By Covariate Dependent Mixtures," Econometric Theory, Cambridge University Press, vol. 30(03), pages 606-646, June.
    8. Conley, Timothy G. & Hansen, Christian B. & McCulloch, Robert E. & Rossi, Peter E., 2008. "A semi-parametric Bayesian approach to the instrumental variable problem," Journal of Econometrics, Elsevier, vol. 144(1), pages 276-305, May.
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    Cited by:

    1. Debdeep Pati & David Dunson, 2014. "Bayesian nonparametric regression with varying residual density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 1-31, February.

    More about this item

    Keywords

    Bayesian semiparametrics; Bayesian conditional density estimation; heteroscedastic linear reggression; posterior consistency;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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