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Communication-efficient sparse composite quantile regression for distributed data

Author

Listed:
  • Yaohong Yang

    (Nankai University)

  • Lei Wang

    (Nankai University)

Abstract

Composite quantile regression (CQR) estimator is a robust and efficient alternative to the M-estimator and ordinary quantile regression estimator in linear models. In order to construct sparse CQR estimation in the presence of distributed data, we propose a penalized communication-efficient surrogate loss function that is computationally superior to the original global loss function. The proposed method only needs the worker machines to compute the gradient based on local data without a penalty and the central machine to solve a regular estimation problem. We prove that the estimation errors based on the proposed method match the estimation error bound of the centralized method by analyzing the entire data set simultaneously. A modified alternating direction method of multipliers algorithm is developed to efficiently obtain the sparse CQR estimator. The performance of the proposed estimator is studied through simulation, and an application to a real data set is also presented.

Suggested Citation

  • Yaohong Yang & Lei Wang, 2023. "Communication-efficient sparse composite quantile regression for distributed data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(3), pages 261-283, April.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:3:d:10.1007_s00184-022-00868-z
    DOI: 10.1007/s00184-022-00868-z
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    References listed on IDEAS

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    2. 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.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    4. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
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