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Bayesian Semiparametric Modelling in Quantile Regression

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  • ATHANASIOS KOTTAS
  • MILOVAN KRNJAJIC

Abstract

We propose a Bayesian semiparametric methodology for quantile regression modelling. In particular, working with parametric quantile regression functions, we develop Dirichlet process mixture models for the error distribution in an additive quantile regression formulation. The proposed non-parametric prior probability models allow the shape of the error density to adapt to the data and thus provide more reliable predictive inference than models based on parametric error distributions. We consider extensions to quantile regression for data sets that include censored observations. Moreover, we employ dependent Dirichlet processes to develop quantile regression models that allow the error distribution to change non-parametrically with the covariates. Posterior inference is implemented using Markov chain Monte Carlo methods. We assess and compare the performance of our models using both simulated and real data sets. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.

Suggested Citation

  • Athanasios Kottas & Milovan Krnjajic, 2009. "Bayesian Semiparametric Modelling in Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 297-319.
  • Handle: RePEc:bla:scjsta:v:36:y:2009:i:2:p:297-319
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    References listed on IDEAS

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    1. 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.
    2. Gelfand, Alan E. & Kottas, Athanasios & MacEachern, Steven N., 2005. "Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1021-1035, September.
    3. Brunner, Lawrence J., 1992. "Bayesian nonparametric methods for data from a unimodal density," Statistics & Probability Letters, Elsevier, vol. 14(3), pages 195-199, June.
    4. Fernando A. Quintana & Pilar L. Iglesias, 2003. "Bayesian clustering and product partition models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 557-574.
    5. 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.
    6. Martin B. Hansen, 2002. "Nonparametric Bayes inference for concave distribution functions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(1), pages 110-127.
    7. Alan E. Gelfand & Athanasios Kottas, 2003. "Bayesian Semiparametric Regression for Median Residual Life," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 651-665.
    8. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
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    Cited by:

    1. Genya Kobayashi & Hideo Kozumi, 2012. "Bayesian analysis of quantile regression for censored dynamic panel data," Computational Statistics, Springer, vol. 27(2), pages 359-380, June.
    2. repec:bla:istatr:v:84:y:2016:i:3:p:359-362 is not listed on IDEAS
    3. Xianhua Dai & Wolfgang Karl Härdle & Keming Yu, 2014. "Do Maternal Health Problems Influence Child's Worrying Status? Evidence from British Cohort Study," SFB 649 Discussion Papers SFB649DP2014-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Das, Priyam & Ghosal, Subhashis, 2017. "Bayesian quantile regression using random B-spline series prior," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 121-143.
    5. Thompson, Paul & Cai, Yuzhi & Moyeed, Rana & Reeve, Dominic & Stander, Julian, 2010. "Bayesian nonparametric quantile regression using splines," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1138-1150, April.
    6. Alhamzawi, Rahim & Yu, Keming, 2013. "Conjugate priors and variable selection for Bayesian quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 209-219.
    7. repec:spr:jagbes:v:22:y:2017:i:4:d:10.1007_s13253-017-0293-6 is not listed on IDEAS
    8. repec:eee:eneeco:v:67:y:2017:i:c:p:60-71 is not listed on IDEAS
    9. repec:spr:aistmt:v:70:y:2018:i:3:d:10.1007_s10463-017-0599-8 is not listed on IDEAS
    10. Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.
    11. Alhamzawi, Rahim, 2016. "Bayesian model selection in ordinal quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 68-78.
    12. repec:bla:istatr:v:84:y:2016:i:3:p:327-344 is not listed on IDEAS

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