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Gibbs Sampling Methods for Bayesian Quantile Regression

Author

Listed:
  • Hideo Kozumi

    (Graduate School of Business Administration, Kobe University)

  • Genya Kobayashi

    (Graduate School of Business Administration, Kobe University)

Abstract

This paper considers quantile regression models using an asymmetric Laplace distribution from a Bayesian point of view. We develop a simple and efficient Gibbs sampling algorithm for fitting the quantile regression model based on a location-scale mixture representation of the asymmetric Laplace distribution. It is shown that the resulting Gibbs sampler can be accomplished by sampling from either normal or generalized inverse Gaussian distribution. We also discuss some possible extensions of our approach, including the incorporation of a scale parameter, the use of double exponential prior, and a Bayesian analysis of Tobit quantile regression. The proposed methods are illustrated by both simulated and real data.

Suggested Citation

  • Hideo Kozumi & Genya Kobayashi, 2009. "Gibbs Sampling Methods for Bayesian Quantile Regression," Discussion Papers 2009-02, Kobe University, Graduate School of Business Administration.
    • Handle: RePEc:kbb:dpaper:2009-02
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    File URL: https://www.b.kobe-u.ac.jp/papers_files/2009_02.pdf
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    References listed on IDEAS

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    1. Wang, Peiming & Cockburn, Iain M & Puterman, Martin L, 1998. "Analysis of Patent Data--A Mixed-Poisson-Regression-Model Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(1), pages 27-41, January.
    2. Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649, Elsevier.
    3. Bronwyn H. Hall & Clint Cumminq & Elizabeth S. Laderman & Joy Mundy, 1988. "The R&D Master File Documentation," NBER Technical Working Papers 0072, National Bureau of Economic Research, Inc.
    4. Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, vol. 66(3), pages 653-672, May.
    5. Bilias, Yannis & Chen, Songnian & Ying, Zhiliang, 2000. "Simple resampling methods for censored regression quantiles," Journal of Econometrics, Elsevier, vol. 99(2), pages 373-386, December.
    6. Kottas A. & Gelfand A.E., 2001. "Bayesian Semiparametric Median Regression Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1458-1468, December.
    7. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    8. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-799, July.
    9. Stephen Walker & Bani K. Mallick, 1999. "A Bayesian Semiparametric Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 55(2), pages 477-483, June.
    10. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(1), pages 105-121, February.
    11. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
    12. Chib, Siddhartha, 1992. "Bayes inference in the Tobit censored regression model," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 79-99.
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