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Bayesian Semiparametric Regression

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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.

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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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Bibliographic Info

Paper provided by Institute for Advanced Studies in its series Economics Series with number 285.

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Length: 41 pages
Date of creation: Apr 2012
Date of revision:
Handle: RePEc:ihs:ihsesp:285

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Related research

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

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References

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  1. Geweke, John & Amisano, Gianni, 2007. "Hierarchical Markov normal mixture models with applications to financial asset returns," Working Paper Series 0831, European Central Bank.
  2. Yeonseung Chung & David Dunson, 2011. "The local Dirichlet process," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(1), pages 59-80, February.
  3. 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.
  4. Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March.
  5. Geweke, John & Keane, Michael, 2007. "Smoothly mixing regressions," Journal of Econometrics, Elsevier, vol. 138(1), pages 252-290, May.
  6. 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.
  7. 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.
  8. repec:cup:cbooks:9780521496032 is not listed on IDEAS
  9. David B. Dunson & Ju-Hyun Park, 2008. "Kernel stick-breaking processes," Biometrika, Biometrika Trust, vol. 95(2), pages 307-323.
  10. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
  11. Chung, Yeonseung & Dunson, David B., 2009. "Nonparametric Bayes Conditional Distribution Modeling With Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1646-1660.
  12. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
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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, vol. 66(1), pages 1-31, February.

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