Covariate-adjusted Expected Shortfall under Data Heterogeneity

随机变量的预期短缺是低于或高于由分位数指定的给定阈值的尾部平均值，并且当主要关注低值或高值结局时，它成为自然和有用的汇总统计量，这在风险评估和治疗效果检测中经常出现。鉴于新兴的重要性，预期短缺作为一个总结措施，最近的文献在金融计量经济学，统计学和运筹学集中在预期短缺回归，它使人们能够评估调整协变量或可能的混杂因素后的尾部差异。该项目将研究协变量调整后的预期短缺的估计，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的统计人员和数据科学家，并将开发一种估计经协变量调整后的预期短缺的新方法，这种方法在计算上是可行和灵活的，能很好地适应数据的异质性，并能进行有效的统计推断。所提出的方法是建立在一个分位数损失函数的基础上的预期短缺的表征，但不依赖于分位数函数本身。当期望的短缺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率从期望的短缺的初始估计开始，并且从凸优化获得更好的解决方案。所提出的方法在弱建模假设下工作，并打开了一个新的机会窗口，更好的统计推断预期的短缺regression.This奖项反映了NSF的法定使命，并已被认为是值得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的支持。

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.