Title: Robust estimation and inference for expected shortfall regression
Authors: Wenxin Zhou - University of California San Diego (United States) [presenting]
Kean Ming Tan - University of Michigan (United States)
Xuming He - University of Michigan (United States)
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, namely its Value-at-Risk (VaR). 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 instabilities, and thus 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 heavy-tailed data) and computationally efficient two-step procedure for fitting joint quantile and ES regression models. Under increasing-dimensional settings, we establish explicit non-asymptotic bounds on estimation and Gaussian approximation errors, which lay the foundation for statistical inference of ES regression. Numerical studies demonstrate the superior statistical performance and numerical efficiency of the proposed method.