A Selective Overview of Quantile Regression for Large-Scale Data

Shanshan Wang, Wei Cao, Xiaoxue Hu (), Hanyu Zhong and Weixi Sun
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Shanshan Wang: School of Economics and Management, 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

Mathematics, 2025, vol. 13, issue 5, 1-30

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.

Keywords: large-scale data; quantile regression; distributed computing; subsampling methods; renewable estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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