随机对象的单调响应
Monotone Response for Random Objects
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中文总结 AI 辅助
本文针对现有单调识别分析仅聚焦标量结果的局限，开发统一框架实现一般度量空间随机对象的部分识别，通过实证示例验证了其有效性。
中文摘要 AI 辅助
单调处理响应（MTR）、单调处理选择（MTS）和单调工具变量（MIV）假设被广泛用于部分识别反事实平均结果，但现有分析几乎仅聚焦于标量结果。我们开发了一个统一框架，用于在这些单调性约束下对取值于一般度量空间的结果进行部分识别，方法是将该度量空间嵌入L²空间，并对嵌入的函数施加逐坐标单调性。该框架为广泛类别的随机对象空间中的Fréchet均值生成有效的识别集，还针对Wasserstein度量下的分布结果、由支撑函数表示的区间值结果、Aitchison度量下的成分结果给出了尖锐的识别结果。我们还在联合MTR-MTS假设下建立了识别集的无支撑刻画。基于Job Corps收入数据和美国国家健康与营养检查调查的牙周健康分布的数值及实证示例，证明了该框架的实用价值。
英文摘要
Monotone treatment response (MTR), monotone treatment selection (MTS), and monotone instrumental variable (MIV) assumptions are widely used to partially identify counterfactual mean outcomes, but existing analyses have focused almost exclusively on scalar outcomes. We develop a unified framework for partial identification with outcomes that take values in a general metric space under these monotonicity restrictions by embedding the metric space into an $L^2$ space and imposing coordinatewise monotonicity on the embedded functions. The proposed framework yields valid identified sets for Fréchet means in a broad class of random-object spaces and further delivers sharp identification results for distributional outcomes under the Wasserstein metric, interval-valued outcomes represented by support functions, and compositional outcomes under the Aitchison metric. We also establish a support-free characterization of the identified set under the joint MTR--MTS assumption. Numerical and empirical illustrations based on Job Corps earnings data and periodontal health distributions from the National Health and Nutrition Examination Survey demonstrate the empirical usefulness of the proposed framework.
