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

Author

Listed:
  • Yanke Wu

    (Guangdong Ocean University
    Renmin University of China)

  • Maozai Tian

    (Renmin University of China
    Lanzhou University of Finance and Economics
    Xinjiang University of Finance and Economics)

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-017-0749-8
    DOI: 10.1007/s00180-017-0749-8
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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. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Koenker, Roger, 1984. "A note on L-estimates for linear models," Statistics & Probability Letters, Elsevier, vol. 2(6), pages 323-325, December.
    4. 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.
    5. Bo Kai & Runze Li & Hui Zou, 2010. "Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 49-69, January.
    6. Brian J. Reich & Luke B. Smith, 2013. "Bayesian Quantile Regression for Censored Data," Biometrics, The International Biometric Society, vol. 69(3), pages 651-660, September.
    7. 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.
    8. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
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