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Bayesian Semiparametric Modelling in Quantile Regression

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  • ATHANASIOS KOTTAS
  • MILOVAN KRNJAJIC
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    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.

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    Bibliographic Info

    Article provided by Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.

    Volume (Year): 36 (2009)
    Issue (Month): 2 ()
    Pages: 297-319

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    Handle: RePEc:bla:scjsta:v:36:y:2009:i:2:p:297-319

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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. Mauro Bernardi & Ghislaine Gayraud & Lea Petrella, 2013. "Bayesian inference for CoVaR," Papers 1306.2834, arXiv.org, revised Nov 2013.
    3. 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.
    4. 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.

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