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Robust communication-efficient distributed composite quantile regression and variable selection for massive data

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  • Wang, Kangning
  • Li, Shaomin
  • Zhang, Benle

Abstract

Statistical analysis of massive data is becoming more and more common. Distributed composite quantile regression (CQR) for massive data is proposed in this paper. Specifically, the global CQR loss function is approximated by a surrogate one on the first machine, which relates to the local data only through their gradients, then the estimator is obtained on the first machine by minimizing the surrogate loss. Because the gradients of local datasets can be efficiently communicated, the communication cost is significantly reduced. In order to reduce the computational burdens, the induced smoothing method is applied. Theoretically, the resulting estimator is proved to be statistically as efficient as the global CQR estimator. What is more, as a direct application, a smooth-threshold distributed CQR estimating equations for variable selection is proposed. The new methods inherit the robustness and efficiency advantages of CQR. The promising performances of the new methods are supported by extensive numerical examples and real data analysis.

Suggested Citation

  • Wang, Kangning & Li, Shaomin & Zhang, Benle, 2021. "Robust communication-efficient distributed composite quantile regression and variable selection for massive data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:csdana:v:161:y:2021:i:c:s0167947321000967
    DOI: 10.1016/j.csda.2021.107262
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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. Kangning Wang & Lu Lin, 2019. "Robust and efficient estimator for simultaneous model structure identification and variable selection in generalized partial linear varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 60(5), pages 1649-1676, October.
    3. Rong Jiang & Wei-Min Qian & Zhan-Gong Zhou, 2016. "Single-index composite quantile regression with heteroscedasticity and general error distributions," Statistical Papers, Springer, vol. 57(1), pages 185-203, March.
    4. Yan Fan & Wolfgang Karl Härdle & Weining Wang & Lixing Zhu, 2018. "Single-Index-Based CoVaR With Very High-Dimensional Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 212-226, April.
    5. Chen, Lanjue & Zhou, Yong, 2020. "Quantile regression in big data: A divide and conquer based strategy," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    6. 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.
    7. 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.
    8. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    9. Zhao, Weihua & Lian, Heng & Song, Xinyuan, 2017. "Composite quantile regression for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 15-33.
    10. Masao Ueki, 2009. "A note on automatic variable selection using smooth-threshold estimating equations," Biometrika, Biometrika Trust, vol. 96(4), pages 1005-1011.
    11. B. M. Brown & You-Gan Wang, 2005. "Standard errors and covariance matrices for smoothed rank estimators," Biometrika, Biometrika Trust, vol. 92(1), pages 149-158, March.
    12. Michael I. Jordan & Jason D. Lee & Yun Yang, 2019. "Communication-Efficient Distributed Statistical Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 668-681, April.
    13. 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.
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