Quantile Regression Models and Their Applications: A Review

Quantile regression (QR) has received increasing attention in recent years and applied to wide areas such as investment, finance, economics, medicine and engineering. Compared with conventional mean regression, QR can characterize the entire conditional distribution of the outcome variable, may be more robust to outliers and misspecification of error distribution, and provides more comprehensive statistical modeling than traditional mean regression. QR models could not only be used to detect heterogeneous effects of covariates at different quantiles of the outcome, but also offer more robust and complete estimates compared to the mean regression, when the normality assumption violated or outliers and long tails exist. These advantages make QR attractive and are extended to apply for different types of data, including independent data, time-to-event data and longitudinal data. Consequently, we present a brief review of QR and its related models and methods for different types of data in various application areas.