High-Dimensional Expected Shortfall Regression
提出套索惩罚期望短缺回归方法，用于高维协变量下响应变量尾部平均的建模与推断，通过数值研究和健康差异数据应用验证效果。
Expected shortfall is defined as the average over the tail below (or above) a certain quantile of a probability distribution. 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 high-dimensional covariates, is often of importance. Under sparse models, we propose the lasso-penalized expected shortfall regression and establish non-asymptotic error bounds, depending explicitly on the sample size, dimension, and sparsity, for the proposed estimator. To perform statistical inference on a covariate of interest, we propose a debiased estimator and establish its asymptotic normality, from which asymptotically valid tests can be constructed. We illustrate the finite sample performance of the proposed method through numerical studies and a data application on health disparity. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.