Robust Estimation and Inference for Expected Shortfall Regression with Many Regressors

TL;DR

This paper introduces a robust and efficient two-step method for joint quantile and Expected Shortfall regression, addressing computational challenges and providing statistical guarantees in high-dimensional settings.

Contribution

It proposes a Neyman-orthogonal score-based approach for stable estimation of ES regression with many regressors, improving robustness and computational efficiency.

Findings

Method achieves robustness to skewed and heavy-tailed data.

Provides explicit non-asymptotic error bounds.

Demonstrates effectiveness through numerical experiments and real data.

Abstract

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.