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Conjugate priors and variable selection for Bayesian quantile regression

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  • Alhamzawi, Rahim
  • Yu, Keming
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    Abstract

    Bayesian variable selection in quantile regression models is often a difficult task due to the computational challenges and non-availability of conjugate prior distributions. These challenges are rarely addressed via either penalized likelihood function or stochastic search variable selection. These methods typically use symmetric prior distributions such as a normal distribution or a Laplace distribution for regression coefficients, which may be suitable for median regression. However, an extreme quantile regression should have different regression coefficients from the median regression, and thus the priors for quantile regression should depend on the quantile. In this article an extension of the Zellners prior which allows for a conditional conjugate prior and quantile dependent prior on Bayesian quantile regression is proposed. Secondly, a novel prior based on percentage bend correlation for model selection is also used in Bayesian regression for the first time. Thirdly, a new variable selection method based on a Gibbs sampler is developed to facilitate the computation of the posterior probabilities. The proposed methods are justified mathematically and illustrated with both simulation and real data.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 64 (2013)
    Issue (Month): C ()
    Pages: 209-219

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    Handle: RePEc:eee:csdana:v:64:y:2013:i:c:p:209-219

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Asymmetric Laplace distribution; g-prior; Gibbs sampler; Model selection; Quantile regression;

    References

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    1. 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.
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    7. Rand Wilcox, 1994. "The percentage bend correlation coefficient," Psychometrika, Springer, vol. 59(4), pages 601-616, December.
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    12. Komunjer, Ivana, 2002. "Quasi-Maximum Likelihood Estimation for Conditional Quantiles," Working Papers 1139, California Institute of Technology, Division of the Humanities and Social Sciences.
    13. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    14. D. F. Benoit & D. Van Den Poel, 2010. "Binary quantile regression: A Bayesian approach based on the asymmetric Laplace density," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 10/662, Ghent University, Faculty of Economics and Business Administration.
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    Cited by:
    1. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
    2. Yves S. Schüler, 2014. "Asymmetric Effects of Uncertainty over the Business Cycle: A Quantile Structural Vector Autoregressive Approach," Working Paper Series of the Department of Economics, University of Konstanz 2014-02, Department of Economics, University of Konstanz.

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