题目：Robust Estimation and Inference for Joint Quantile and Expected Shortfall Regression

主讲人：加州大学圣地亚哥分校 周文心副教授

主持人：统计学院 常晋源教授

时间：2022年4月12日（周二）上午10:00-11:00

地点：腾讯会议，313 180 169

报告摘要：

Expected Shortfall (ES), as a financial term, refers to the average return on a risky asset conditional on the return below certain quantile of its distribution. The latter is also known as the Value-at-Risk (VaR). In their Fundamental Review of the Trading Book (Basel Committee, 2016, 2019), the Basel Committee on Banking Supervision confirmed the replacement of VaR with ES as the standard risk measure in banking and insurance. From a statistical perspective, we consider a linear regression framework that simultaneously models the quantile and the ES of a response variable given a set of covariates. Existing approach is based on minizming a joint loss function, which is not only discontinuous but also non-convex. This inevitably 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 computationally efficient two-step procedure and its robust variant for joint quantile and ES regression. 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. In high-dimensional sparse settings, we study the theoretical properties of regulaized two-step ES regression estimator as well as its robust counterpart. This paves the way for developing post-selection inference methods for high-dimensional joint QR and ES regression.

主讲人简介：

I am currently an Associate Professor in the Department of Mathematics at University of California, San Diego. I graduated from HKUST in 2013, and was a postdoc from 2013 to 2017 at the University of Melbourne and Princeton University. My research interests are high-dimensional statistical inference, robust and quantile regressions.