This talk introduces the innovative concept of Average Quantile Regression (AQR), which not only applies to regression model beyond mean but also serves as a coherent risk measure. Many traditional regression models beyond mean and risk measures can be viewed as special cases of AQR. As a flexibly non-parametric regression model, AQR demonstrates outstanding performance in handling high-dimensional and large datasets, particularly those generated by distributed systems, offering a convenient framework for their statistical analysis. We derive the corresponding estimators and develop their asymptotic properties. Simulations and real data analyses are conducted to illustrate the finite-sample performance of the proposed methods.
