Computational Statistics

, Volume 32, Issue 4, pp 1375–1393 | Cite as

An effective method to reduce the computational complexity of composite quantile regression

Original Paper


In this article, we aim to reduce the computational complexity of the recently proposed composite quantile regression (CQR). We propose a new regression method called infinitely composite quantile regression (ICQR) to avoid the determination of the number of uniform quantile positions. Unlike the composite quantile regression, our proposed ICQR method allows combining continuous and infinite quantile positions. We show that the proposed ICQR criterion can be readily transformed into a linear programming problem. Furthermore, the computing time of the ICQR estimate is far less than that of the CQR, though it is slightly larger than that of the quantile regression. The oracle properties of the penalized ICQR are also provided. The simulations are conducted to compare different estimators. A real data analysis is used to illustrate the performance.


Quantile regression Composite quantile regression Computational complexity Linear programming Dual problem 



The work was partially supported by the major research Projects of philosophy and social science of the Chinese Ministry of Education (No. 15JZD015), National Natural Science Foundation of China (No. 11271368), Project supported by the Major Program of Beijing Philosophy and Social Science Foundation of China (No. 15ZDA17), Project of Ministry of Education supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20130004110007), the Key Program of National Philosophy and Social Science Foundation Grant (No. 13AZD064), the Major Project of Humanities Social Science Foundation of Ministry of Education (No. 15JJD910001), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (No. 15XNL008)


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.College of ScienceGuangdong Ocean UniversityZhanjiangChina
  2. 2.Center for Applied Statistics, School of StatisticsRenmin University of ChinaBeijingChina
  3. 3.School of StatisticsLanzhou University of Finance and EconomicsLanzhouChina
  4. 4.School of Statistics and InformationXinjiang University of Finance and EconomicsÜrümqiChina

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