Covariate-adjusted Expected Shortfall under Data Heterogeneity

随机变量的预期不足是指低于或高于由分位数指定的给定阈值的尾部平均值，当主要关注低值或高值结果时，它就成为一个自然而有用的汇总统计，就像风险评估和治疗效果检测中经常出现的情况一样。考虑到预期缺口作为一种总结性度量的重要性，最近在金融计量经济学、统计学和运筹学方面的文献都集中在预期缺口回归上，它使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后预期缺口的估计，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循证分析提供工具包，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后的预期缺口，这种方法在计算上是可行和灵活的，可以很好地适应数据异质性，并允许有效的统计推断。所提出的方法是建立在基于分位数损失函数的预期缺口特征的基础上，但不依赖于分位数函数本身。当期望缺口函数采用参数形式时，所提出的方法将以可能的次优收敛速度从期望缺口的初始估计开始，并从凸优化中获得更好的解。该方法适用于弱建模假设，为期望不足回归的更好的统计推断打开了新的窗口。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识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.