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A Selective Overview of Quantile Regression for Large-Scale Data

Author

Listed:
  • Shanshan Wang

    (School of Economics and Management, Beihang University, Beijing 100191, China
    MOE Key Laboratory of Complex System Analysis and Management Decision, Beihang University, Beijing 100191, China)

  • Wei Cao

    (School of Economics and Management, Beihang University, Beijing 100191, China)

  • Xiaoxue Hu

    (School of Economics and Management, Beihang University, Beijing 100191, China)

  • Hanyu Zhong

    (School of Economics and Management, Beihang University, Beijing 100191, China)

  • Weixi Sun

    (School of Economics and Management, Beihang University, Beijing 100191, China
    Sino-French Engineering School, Beihang University, Beijing 100191, China)

Abstract

Large-scale data, characterized by heterogeneity due to heteroskedastic variance or inhomogeneous covariate effects, arises in diverse fields of scientific research and technological development. Quantile regression (QR) is a valuable tool for detecting heteroskedasticity, and numerous QR statistical methods for large-scale data have been rapidly developed. This paper provides a selective review of recent advances in QR theory, methods, and implementations, particularly in the context of massive and streaming data. We focus on three key strategies for large-scale QR analysis: (1) distributed computing, (2) subsampling methods, and (3) online updating. The main contribution of this paper is a comprehensive review of existing work and advancements in these areas, addressing challenges such as managing the non-smooth QR loss function, developing distributed and online updating formulations, and conducting statistical inference. Finally, we highlight several issues that require further study.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:837-:d:1603908
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