Statistics Department Seminar Series
Abstract: The expected shortfall is defined as the average over the tail below (or above) a certain quantile of a probability distribution. The expected shortfall regression provides powerful tools for learning the relationship between a response variable and a set of covariates while exploring the heterogeneous effects of the covariates. In the health disparity research, for example, the lower/upper tail of the conditional distribution of a health-related outcome, given covariates, is often of importance. Motivated by the idea of using Neyman-orthogonal scores to reduce sensitivity to nuisance parameters, we consider a computationally efficient two-step procedure for estimating the expected shortfall regression coefficients. We establish explicit non-asymptotic bounds on the resulting estimator that lay down the foundation for performing statistical inference under different scenarios: (i) classical setting with $p<n$; (ii) high-dimensional setting with $p>n$; and (iii) under heavy-tailed random noise.