A Selective Overview of Quantile Regression for Large-scale Data

Large-scale data characterized by heterogeneity due to heteroscedastic 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 developed rapidly. 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.