High-Dimensional Expected Shortfall Regression

• 成果类型: Article; Early Access
• 署名作者: Zhang, Shushu; He, Xuming; Tan, Kean Ming; Zhou, Wen-Xin
• 署名单位: University of Michigan System; University of Michigan; Washington University (WUSTL); University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2448860
• 发表日期: 2025
• 关键词: tuning parameter selection; variable selection; confidence-regions; model selection; lung-cancer; cotinine; RISK; quantile; criteria; tests

摘要

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.