Covariate-adjusted Expected Shortfall under Data Heterogeneity

随机变量的预期不足是尾部平均值低于或高于分位数指定的给定阈值，当低值或高值结果是主要关注点时（风险评估和治疗效果检测中经常出现这种情况），它就成为自然且有用的汇总统计量。鉴于预期缺口作为一种综合衡量指标的重要性日益凸显，金融计量经济学、统计学和运筹学领域的最新文献都集中在预期缺口回归上，这使得人们能够在调整协变量或可能的混杂因素后评估尾部差异。该项目将研究协变量调整预期缺口的估计，确定新的估计方法，并研究其适应数据异质性的统计特性。拟议的研究将为不同领域的数据驱动和基于证据的分析提供工具包，包括脑震荡研究、健康差异研究和气候研究。该项目还将有助于培训新一代统计学家和数据科学家。该项目将开发一种新的方法来估计协变量调整的预期缺口，该方法在计算上可行且灵活，能够很好地适应数据异质性，并允许有效的统计推断。所提出的方法建立在基于分位数损失函数的预期缺口的表征之上，但不依赖于分位数函数本身。当预期缺口函数采用参数形式时，所提出的方法将从预期缺口的初始估计量开始，收敛速度可能是次优的，并从凸优化中获得更好的解决方案。所提出的方法在弱建模假设下工作，并为更好地统计推断预期缺口回归打开了一个新的机会之窗。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

The expected shortfall of a random variable is the tail average below or above a given threshold specified by a quantile, and it becomes a natural and useful summary statistic when low- or high-valued outcomes are of primary interest, as is often the case in risk assessment and treatment effect detection. Given the emerging importance of the expected shortfall as a summary measure, the recent literature in financial econometrics, statistics and operations research has focused on the expected shortfall regression, which enables one to evaluate the tail differences after adjusting for the covariates or possible confounding factors. The project will study the estimation of covariate-adjusted expected shortfall, identify new approaches for estimation, and study the statistical properties for its adaptation to data heterogeneity. The proposed research will provide toolkit for data-driven and evidence-based analysis in diverse fields, including concussion research, health disparity research, and climate studies. The project will also contribute to the training of a new generation of statisticians and data scientists.The project will develop a new approach to estimation of covariate-adjusted expected shortfall that is computationally feasible and flexible, adapts well to data heterogeneity, and allows effective statistical inference. The proposed approach is built on a characterization of the expected shortfall based on a quantile loss function, but without reliance on the quantile function itself. When the expected shortfall function takes a parametric form, the proposed approach will start with an initial estimator of the expected shortfall at possibly a sub-optimal rate of convergence and obtain a much better solution from convex optimization. The proposed method works under weak modeling assumptions and opens a new window of opportunities for better statistical inference for expected shortfall regression.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.