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Bayesian adaptive Lasso quantile regression

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  • R. ALHAMZAWI

    ()

  • K. YU
  • D. F. BENOIT

Abstract

Recently, variable selection by penalized likelihood has attracted much research interest. In this paper, we propose adaptive Lasso quantile regression (BALQR) from a Bayesian perspective. The method extends the Bayesian Lasso quantile regression by allowing different penalization parameters for different regression coefficients. Inverse gamma prior distributions are placed on the penalty parameters. We treat the hyperparameters of the inverse gamma prior as unknowns and estimate them along with the other parameters. A Gibbs sampler is developed to simulate the parameters from the posterior distributions. Through simulation studies and analysis of a prostate cancer data set, we compare the performance of the BALQR method proposed with six existing Bayesian and non-Bayesian methods. The simulation studies and the prostate cancer data analysis indicate that the BALQR method performs well in comparision to the other approaches.

Suggested Citation

  • R. Alhamzawi & K. Yu & D. F. Benoit, 2011. "Bayesian adaptive Lasso quantile regression," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 11/728, Ghent University, Faculty of Economics and Business Administration.
  • Handle: RePEc:rug:rugwps:11/728
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    File URL: http://wps-feb.ugent.be/Papers/wp_11_728.pdf
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. 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.
    3. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    4. Wang, Hansheng & Li, Guodong & Jiang, Guohua, 2007. "Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 347-355, July.
    5. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    6. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, December.
    7. Chris Hans, 2009. "Bayesian lasso regression," Biometrika, Biometrika Trust, vol. 96(4), pages 835-845.
    8. Hideo Kozumi & Genya Kobayashi, 2009. "Gibbs Sampling Methods for Bayesian Quantile Regression," Discussion Papers 2009-02, Kobe University, Graduate School of Business Administration.
    9. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    10. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    11. Yu, Keming & Stander, Julian, 2007. "Bayesian analysis of a Tobit quantile regression model," Journal of Econometrics, Elsevier, vol. 137(1), pages 260-276, March.
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    Citations

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    Cited by:

    1. Zhao, Kaifeng & Lian, Heng, 2016. "The Expectation–Maximization approach for Bayesian quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 1-11.
    2. Vahid Nassiri & Ignace Loris, 2014. "An efficient algorithm for structured sparse quantile regression," Computational Statistics, Springer, vol. 29(5), pages 1321-1343, October.
    3. repec:bla:istatr:v:84:y:2016:i:3:p:327-344 is not listed on IDEAS
    4. Hussein Hashem & Veronica Vinciotti & Rahim Alhamzawi & Keming Yu, 2016. "Quantile regression with group lasso for classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(3), pages 375-390, September.
    5. Yuzhu Tian & Er’qian Li & Maozai Tian, 2016. "Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates," Computational Statistics, Springer, vol. 31(3), pages 1031-1057, September.
    6. B. Dima & Ş. M. Dima, 2016. "Income Distribution and Social Tolerance," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 128(1), pages 439-466, August.
    7. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
    8. repec:spr:stpapr:v:58:y:2017:i:4:d:10.1007_s00362-015-0737-4 is not listed on IDEAS

    More about this item

    Keywords

    Gibbs sampler; Lasso; Quantile regression; Skewed Laplace distribution.;

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