讲座题目：Expected Shortfall Regression

主 讲 人：周文心

讲座时间：2022年5月12日（周四）上午9:30-10:30

地点：线上：腾讯会议 ID 954-676-464 

          线下：综合楼644会议室

主讲人简介：

       周文心，加州大学圣地亚哥分校数学系副教授，研究兴趣：高维统计推断，稳健统计分析，分位数回归，和统计机器学习。现担任概率统计顶级期刊Annals of Statistics，Annals of applied Probability，JRSSB的副主编，在AOS、AOP、JRSSB、JASA、JOE等杂志发表多篇高水平学术成果。

讲座摘要：

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). In this work, 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 errros, which lay the foundation for statistical inference of ES regression. Numerical studies demonstrate the superior numerical efficiency of the proposed method.