A Review of Recent Advances in High-Dimensional Quantile Regression

Quantile regression has emerged as a powerful tool for modeling heterogeneous effects and tail behavior across different parts of the response distribution. This review highlights recent advances that address the challenges of high-dimensional and complex data, including penalized estimation, debiasing, distributed learning, transfer learning, and machine learning–based approaches for quantile regression. Practical procedures, theoretical insights, and available software are summarized to support the application of modern quantile regression in diverse data environments. New advances make quantile regression smarter, faster, and ready for complex, high-dimensional data. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical Models > Linear Models Statistical Models > Nonlinear Models.