Conjugate priors and variable selection for Bayesian quantile regression
AbstractBayesian 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 InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 64 (2013)
Issue (Month): C ()
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Web page: http://www.elsevier.com/locate/csda
Asymmetric Laplace distribution; g-prior; Gibbs sampler; Model selection; Quantile regression;
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- 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.
- Smith, M. & Kohn, R., .
"Nonparametric Regression using Bayesian Variable Selection,"
Statistics Working Paper
_009, Australian Graduate School of Management.
- Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
- Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521845731.
- Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
- Yuan, Ming & Lin, Yi, 2005. "Efficient Empirical Bayes Variable Selection and Estimation in Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1215-1225, December.
- Rand Wilcox, 1994. "The percentage bend correlation coefficient," Psychometrika, Springer, vol. 59(4), pages 601-616, December.
- Yu, Keming & Stander, Julian, 2007. "Bayesian analysis of a Tobit quantile regression model," Journal of Econometrics, Elsevier, vol. 137(1), pages 260-276, March.
- Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
- Hanson T. & Johnson W.O., 2002. "Modeling Regression Error With a Mixture of Polya Trees," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1020-1033, December.
- Gerlach, Richard H. & Chen, Cathy W. S. & Chan, Nancy Y. C., 2011.
"Bayesian Time-Varying Quantile Forecasting for Value-at-Risk in Financial Markets,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 29(4), pages 481-492.
- Chan, Nancy Y. C. & Chen, Cathy W.S. & Gerlach, Richard, 2009. "Bayesian time-varying quantile forecasting for Value-at-Risk in financial markets," Working Papers 01/2009, University of Sydney Business School, Discipline of Business Analytics.
- Komunjer, Ivana, 2002.
"Quasi-Maximum Likelihood Estimation for Conditional Quantiles,"
1139, California Institute of Technology, Division of the Humanities and Social Sciences.
- Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
- 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.
- 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.
- Tony Lancaster & Sung Jae Jun, 2010. "Bayesian quantile regression methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 287-307.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
- 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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