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Linear Quantile Regression Based on EM Algorithm

Author

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  • Yuzhu Tian
  • Maozai Tian
  • Qianqian Zhu

Abstract

This article aims to put forward a new method to solve the linear quantile regression problems based on EM algorithm using a location-scale mixture of the asymmetric Laplace error distribution. A closed form of the estimator of the unknown parameter vector β based on EM algorithm, is obtained. In addition, some simulations are conducted to illustrate the performance of the proposed method. Simulation results demonstrate that the proposed algorithm performs well. Finally, the classical Engel data is fitted and the Bootstrap confidence intervals for estimators are provided.

Suggested Citation

  • Yuzhu Tian & Maozai Tian & Qianqian Zhu, 2014. "Linear Quantile Regression Based on EM Algorithm," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(16), pages 3464-3484, August.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:16:p:3464-3484
    DOI: 10.1080/03610926.2013.766339
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    Citations

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    Cited by:

    1. Christian E. Galarza & Panpan Zhang & Víctor H. Lachos, 2021. "Logistic Quantile Regression for Bounded Outcomes Using a Family of Heavy-Tailed Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 325-349, November.
    2. Siamak Ghasemzadeh & Mojtaba Ganjali & Taban Baghfalaki, 2018. "Bayesian quantile regression for analyzing ordinal longitudinal responses in the presence of non-ignorable missingness," METRON, Springer;Sapienza Università di Roma, vol. 76(3), pages 321-348, December.
    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. Yanke Wu & Maozai Tian, 2017. "An effective method to reduce the computational complexity of composite quantile regression," Computational Statistics, Springer, vol. 32(4), pages 1375-1393, December.
    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. Fengkai Yang, 2018. "A Stochastic EM Algorithm for Quantile and Censored Quantile Regression Models," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 555-582, August.
    7. Tian, Yuzhu & Zhu, Qianqian & Tian, Maozai, 2016. "Estimation of linear composite quantile regression using EM algorithm," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 183-191.
    8. Tian, Yuzhu & Song, Xinyuan, 2020. "Bayesian bridge-randomized penalized quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    9. Mai Dao & Min Wang & Souparno Ghosh & Keying Ye, 2022. "Bayesian variable selection and estimation in quantile regression using a quantile-specific prior," Computational Statistics, Springer, vol. 37(3), pages 1339-1368, July.

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