Robust estimation and inference for expected shortfall regression with many regressors.

This article focuses on developing a robust and computationally efficient two-step regression method for estimating expected shortfall (ES), also known as superquantile or conditional value-at-risk, within a joint quantile and ES regression framework. The proposed approach improves upon existing methods by applying adaptive Huber regression in the second step to enhance robustness against heavy-tailed and skewed error distributions, while maintaining statistical efficiency under light-tailed conditions. The authors establish finite-sample theoretical guarantees, including non-asymptotic error bounds, Bahadur representation, and Gaussian approximations, allowing for increasing model dimension with sample size. Numerical experiments and applications to health disparity and the Job Training Partnership Act (JTPA) study demonstrate that the robust two-step estimator achieves superior computational speed, stability, and robustness compared to prior joint M-estimators, and provides complementary insights to quantile regression in analyzing tail behavior of outcomes.