Quantile regression for linear models with autoregressive errors using EM algorithm

  • Yuzhu Tian
  • Manlai Tang
  • Yanchao Zang
  • Maozai Tian
Original Paper


In this paper, we consider the quantile linear regression models with autoregressive errors. By incorporating the expectation–maximization algorithm into the considered model, the iterative weighted least square estimators for quantile regression parameters and autoregressive parameters are derived. Finally, the proposed procedure is illustrated by simulations and a real data example.


Maximum likelihood estimation (MLE) Hierarchical model QR analysis Autoregressive model 



The authors thank editors and two reviewers for their constructive comments and valuable suggestions which have greatly improved the paper. The work is partly supported by Young academic leaders project of Henan University of Science and Technology (No. 13490008), National Natural Science Foundation of China (No. 11501167) and China Postdoctoral Science Foundation (No. 2017M610156).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yuzhu Tian
    • 1
    • 2
  • Manlai Tang
    • 3
  • Yanchao Zang
    • 1
  • Maozai Tian
    • 4
  1. 1.School of Mathematics and StatisticsHenan University of Science and TechnologyLuoYangChina
  2. 2.School of Statistics and MathematicsThe Central University of Finance and EconomicsBeijingChina
  3. 3.Department of Mathematics and StatisticsHang Seng Management CollegeHong KongChina
  4. 4.School of StatisticsRenmin University of ChinaBeijingChina

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