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Distributed quantile regression for longitudinal big data

Author

Listed:
  • Ye Fan

    (Capital University of Economics and Business)

  • Nan Lin

    (Washington University in St. Louis)

  • Liqun Yu

    (Washington University in St. Louis)

Abstract

Longitudinal data, measurements taken from the same subjects over time, appear routinely in many scientific fields, such as biomedical science, public health, ecology and environmental sciences. With the rapid development of information technology, modern longitudinal data are becoming massive in volume and high dimensional, hence often require distributed analysis in real-world applications. Standard divide-and-conquer techniques do not apply directly to longitudinal big data due to within-subject dependence. In this paper, we focus on developing a distributed algorithm to support quantile regression (QR) analysis of longitudinal big data, which currently remains an open and challenging issue. We employ weighted quantile regression (WQR) to accommodate the correlation in longitudinal big data, and parallelize the WQR estimation process with a two-stage algorithm to support distributed computing. Based on weights estimated in the first stage by the Newton–Raphson algorithm, the second stage solves the WQR problem using the multi-block alternating direction method of multipliers (ADMM). Simulation studies show that, compared to traditional non-distributed algorithms, our proposed method has favorable estimation accuracy and is computationally more efficient in both non-distributed and distributed environments. Further, we also analyze an air quality data set to illustrate the practical performance of this method.

Suggested Citation

  • Ye Fan & Nan Lin & Liqun Yu, 2024. "Distributed quantile regression for longitudinal big data," Computational Statistics, Springer, vol. 39(2), pages 751-779, April.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:2:d:10.1007_s00180-022-01318-0
    DOI: 10.1007/s00180-022-01318-0
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    References listed on IDEAS

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    1. Liqun Yu & Nan Lin, 2017. "ADMM for Penalized Quantile Regression in Big Data," International Statistical Review, International Statistical Institute, vol. 85(3), pages 494-518, December.
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    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    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. Fu, Liya & Wang, You-Gan, 2012. "Quantile regression for longitudinal data with a working correlation model," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2526-2538.
    7. Haiying Wang & Yanyuan Ma, 2021. "Optimal subsampling for quantile regression in big data," Biometrika, Biometrika Trust, vol. 108(1), pages 99-112.
    8. Zhao, Weihua & Lian, Heng & Song, Xinyuan, 2017. "Composite quantile regression for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 15-33.
    9. Cheng Yong Tang & Chenlei Leng, 2011. "Empirical likelihood and quantile regression in longitudinal data analysis," Biometrika, Biometrika Trust, vol. 98(4), pages 1001-1006.
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    1. Shanshan Wang & Wei Cao & Xiaoxue Hu & Hanyu Zhong & Weixi Sun, 2025. "A Selective Overview of Quantile Regression for Large-Scale Data," Mathematics, MDPI, vol. 13(5), pages 1-30, March.

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