  Expected Shortfall (ES), also known as superquantile or Conditional
Value-at-Risk, has been recognized as an important measure in risk analysis and
stochastic optimization, and is also finding applications beyond these areas.
In finance, it refers to the conditional expected return of an asset given that
the return is below some quantile of its distribution. In this paper, we
consider a recently proposed joint regression framework that simultaneously
models the quantile and the ES of a response variable given a set of
covariates, for which the state-of-the-art approach is based on minimizing a
joint loss function that is non-differentiable and non-convex. This inevitably
raises numerical challenges and limits its applicability for analyzing
large-scale data. Motivated by the idea of using Neyman-orthogonal scores to
reduce sensitivity with respect to nuisance parameters, we propose a
statistically robust (to highly skewed and heavy-tailed data) and
computationally efficient two-step procedure for fitting joint quantile and ES
regression models. With increasing covariate dimensions, we establish explicit
non-asymptotic bounds on estimation and Gaussian approximation errors, which
lay the foundation for statistical inference. Finally, we demonstrate through
numerical experiments and two data applications that our approach well balances
robustness, statistical, and numerical efficiencies for expected shortfall
regression.
