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Distributed Bootstrap Simultaneous Inference for High-Dimensional Quantile Regression

Author

Listed:
  • Xingcai Zhou

    (School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China)

  • Zhaoyang Jing

    (School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China)

  • Chao Huang

    (Department of Statistics, Florida State University, Tallahassee, FL 32306, USA)

Abstract

Modern massive data with enormous sample size and tremendous dimensionality are usually impossible to process with a single machine. They are typically stored and processed in a distributed manner. In this paper, we propose a distributed bootstrap simultaneous inference for a high-dimensional quantile regression model using massive data. Meanwhile, a communication-efficient (CE) distributed learning algorithm is developed via the CE surrogate likelihood framework and ADMM procedure, which can handle the non-smoothness of the quantile regression loss and the Lasso penalty. We theoretically prove the convergence of the algorithm and establish a lower bound on the number of communication rounds ι min that warrant statistical accuracy and efficiency. The distributed bootstrap validity and efficiency are corroborated by an extensive simulation study.

Suggested Citation

  • Xingcai Zhou & Zhaoyang Jing & Chao Huang, 2024. "Distributed Bootstrap Simultaneous Inference for High-Dimensional Quantile Regression," Mathematics, MDPI, vol. 12(5), pages 1-54, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:735-:d:1349007
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    References listed on IDEAS

    as
    1. Chatterjee, A. & Lahiri, S. N., 2011. "Bootstrapping Lasso Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 608-625.
    2. Xianyang Zhang & Guang Cheng, 2017. "Simultaneous Inference for High-Dimensional Linear Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 757-768, April.
    3. Ariel Kleiner & Ameet Talwalkar & Purnamrita Sarkar & Michael I. Jordan, 2014. "A scalable bootstrap for massive data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(4), pages 795-816, September.
    4. Ruben Dezeure & Peter Bühlmann & Cun-Hui Zhang, 2017. "High-dimensional simultaneous inference with the bootstrap," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 685-719, December.
    5. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    6. 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.
    7. Lan Wang & Yichao Wu & Runze Li, 2012. "Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 214-222, March.
    Full references (including those not matched with items on IDEAS)

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