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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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    References listed on IDEAS

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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. Yu-Zhu Tian & Man-Lai Tang & Wai-Sum Chan & Mao-Zai Tian, 2021. "Bayesian bridge-randomized penalized quantile regression for ordinal longitudinal data, with application to firm’s bond ratings," Computational Statistics, Springer, vol. 36(2), pages 1289-1319, June.
    3. Yuzhu Tian & Manlai Tang & Yanchao Zang & Maozai Tian, 2018. "Quantile regression for linear models with autoregressive errors using EM algorithm," Computational Statistics, Springer, vol. 33(4), pages 1605-1625, December.
    4. Rahim Alhamzawi & Haithem Taha Mohammad Ali, 2020. "Brq: an R package for Bayesian quantile regression," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 313-328, December.
    5. Sakae Oya, 2021. "A Bayesian Graphical Approach for Large-Scale Portfolio Management with Fewer Historical Data," Papers 2103.05880, arXiv.org, revised Mar 2022.
    6. Bernardi, Mauro & Bottone, Marco & Petrella, Lea, 2018. "Bayesian quantile regression using the skew exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 92-111.
    7. Seongil Jo & Taeyoung Roh & Taeryon Choi, 2016. "Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 177-206, March.
    8. Tian, Yuzhu & Song, Xinyuan, 2020. "Bayesian bridge-randomized penalized quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    9. Taha Alshaybawee & Habshah Midi & Rahim Alhamzawi, 2017. "Bayesian elastic net single index quantile regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 853-871, April.
    10. Vahid Nassiri & Ignace Loris, 2014. "An efficient algorithm for structured sparse quantile regression," Computational Statistics, Springer, vol. 29(5), pages 1321-1343, October.
    11. Yunwen Yang & Huixia Judy Wang & Xuming He, 2016. "Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood," International Statistical Review, International Statistical Institute, vol. 84(3), pages 327-344, December.
    12. Rahim Alhamzawi & Keming Yu, 2012. "Variable selection in quantile regression via Gibbs sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 799-813, August.
    13. van Erp, Sara & Oberski, Daniel L. & Mulder, Joris, 2018. "Shrinkage priors for Bayesian penalized regression," OSF Preprints cg8fq, Center for Open Science.
    14. 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.
    15. David Kohns & Tibor Szendrei, 2020. "Horseshoe Prior Bayesian Quantile Regression," Papers 2006.07655, arXiv.org, revised Mar 2021.
    16. 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.
    17. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
    18. A. Aghamohammadi & S. Mohammadi, 2017. "Bayesian analysis of penalized quantile regression for longitudinal data," Statistical Papers, Springer, vol. 58(4), pages 1035-1053, December.
    19. Shiyi Tu & Min Wang & Xiaoqian Sun, 2017. "Bayesian variable selection and estimation in maximum entropy quantile regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(2), pages 253-269, January.

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    Keywords

    Gibbs sampler; Lasso; Quantile regression; Skewed Laplace distribution.;
    All these keywords.

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