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Optimal subsampling algorithm for composite quantile regression with distributed data

Author

Listed:
  • Xiaohui Yuan

    (Changchun University of Technology)

  • Shiting Zhou

    (Changchun University of Technology)

  • Yue Wang

    (Changchun University of Technology)

Abstract

For massive data stored on multiple machines, we propose a distributed subsampling procedure for the composite quantile regression. By establishing the consistency and asymptotic normality of the composite quantile regression estimator from a general subsampling algorithm, we derive the optimal subsampling probabilities and the optimal allocation sizes under the L-optimality criteria. A two-step algorithm is developed to approximate the optimal subsampling procedure. The proposed methods are illustrated through numerical experiments on simulated and real datasets.

Suggested Citation

  • Xiaohui Yuan & Shiting Zhou & Yue Wang, 2025. "Optimal subsampling algorithm for composite quantile regression with distributed data," Computational Statistics, Springer, vol. 40(9), pages 4901-4936, December.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:9:d:10.1007_s00180-024-01570-6
    DOI: 10.1007/s00180-024-01570-6
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    References listed on IDEAS

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    1. Xiaohui Yuan & Yong Li & Xiaogang Dong & Tianqing Liu, 2022. "Optimal subsampling for composite quantile regression in big data," Statistical Papers, Springer, vol. 63(5), pages 1649-1676, October.
    2. 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).
    3. Yujing Shao & Lei Wang, 2022. "Optimal subsampling for composite quantile regression model in massive data," Statistical Papers, Springer, vol. 63(4), pages 1139-1161, August.
    4. Zhang, Haixiang & Wang, HaiYing, 2021. "Distributed subdata selection for big data via sampling-based approach," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    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. Jun Yu & HaiYing Wang & Mingyao Ai & Huiming Zhang, 2022. "Optimal Distributed Subsampling for Maximum Quasi-Likelihood Estimators With Massive Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 265-276, January.
    7. Fang Fang & Jiwei Zhao & S. Ejaz Ahmed & Annie Qu, 2021. "A weak‐signal‐assisted procedure for variable selection and statistical inference with an informative subsample," Biometrics, The International Biometric Society, vol. 77(3), pages 996-1010, September.
    8. Kangning Wang & Mengjie Hao & Xiaofei Sun, 2021. "Robust and efficient estimating equations for longitudinal data partial linear models and its applications," Statistical Papers, Springer, vol. 62(5), pages 2147-2168, October.
    9. 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.
    10. Haiying Wang & Yanyuan Ma, 2021. "Optimal subsampling for quantile regression in big data," Biometrika, Biometrika Trust, vol. 108(1), pages 99-112.
    11. Yongxiao Qiu & Guanghui Du & Song Chai, 2020. "A Novel Algorithm for Distributed Data Stream Using Big Data Classification Model," International Journal of Information Technology and Web Engineering (IJITWE), IGI Global Scientific Publishing, vol. 15(4), pages 1-17, October.
    12. Zhao, Weihua & Lian, Heng & Song, Xinyuan, 2017. "Composite quantile regression for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 15-33.
    13. HaiYing Wang & Min Yang & John Stufken, 2019. "Information-Based Optimal Subdata Selection for Big Data Linear Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 393-405, January.
    14. HaiYing Wang & Rong Zhu & Ping Ma, 2018. "Optimal Subsampling for Large Sample Logistic Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 829-844, April.
    15. Lulu Zuo & Haixiang Zhang & HaiYing Wang & Liuquan Sun, 2021. "Optimal subsample selection for massive logistic regression with distributed data," Computational Statistics, Springer, vol. 36(4), pages 2535-2562, December.
    Full references (including those not matched with items on IDEAS)

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