发表机构
University of São Paulo（圣保罗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出Wasserstein因果森林处理分布值结果，定义转换处理效应，模拟显示在多数设计中最准确，应用于STAR数据发现小班提升高分端更多且对弱势学生影响最大。
AI 中文摘要
本文提出了Wasserstein因果森林（WCF），用于处理每个单元的结果本身是概率分布的情况。本研究还定义了有限网格上的转换平均处理效应和条件平均处理效应，包括一个参考距离对比，用于询问处理是否将单元级分布移向预设基准。模拟涵盖了零效应、位置和形状变化、有限重叠、均值相等但分布不同、异质性效应、多模态以及结构零。WCF在大多数报告的设计中，在条件法则度量上最为准确，并在主要的位置和形状设置中显著改善了参考效应估计，但在多模态设置中不如森林基线准确。WCF应用于著名的Project STAR（word1990state），揭示小班不仅改变均值：它们平均将年级内数学成绩提高0.161个标准差（标准误0.028）；但增益并非均匀的位置偏移，在课堂分数分布的上部更大（第九十百分位为+0.179，第十百分位为+0.091），并且在描述性分层估计中，在服务最多经济弱势学生的学校（最高免费午餐四分位，+0.262，其他为+0.092至+0.164）中最大，而整体离散度基本不变。
英文摘要
This paper proposes Wasserstein Causal Forests (WCF) for settings in which each unit's outcome is itself a probability distribution. This study also defines finite-grid transformed average and conditional average treatment effects, including a reference-distance contrast that asks whether treatment moves unit-level distributions toward a prespecified benchmark. Simulations cover null effects, location and shape changes, limited overlap, equal-mean but different laws, heterogeneous effects, multimodality, and structural zeros. WCF is most accurate on the conditional-law metric in most reported designs and sharply improves reference-effect estimation in the principal location-and-shape settings, but it is less accurate than the forest baselines for multimodal settings. WCF is applied to the famous Project STAR \citep{word1990state}, revealing that small classes alter more than the mean: they raise within-grade mathematics achievement by $0.161$ standard deviations on average (SE $0.028$); but the gain is not a uniform location shift, it is larger in the upper part of the classroom score distribution ($+0.179$ at the ninetieth percentile versus $+0.091$ at the tenth) and, in descriptive stratum estimates, largest in the schools serving the most economically disadvantaged students (highest free-lunch quartile, $+0.262$, versus $+0.092$ to $+0.164$ elsewhere), while overall dispersion is essentially unchanged.
