Beyond conditional average treatment effects, treatments may impact the entire outcome distribution in covariate-dependent ways, for example, by altering the variance or tail risks for specific subpopulations. We propose a novel estimand to capture such conditional distributional treatment effects, and develop a doubly robust estimator that is minimax optimal in the local asymptotic sense. Using this, we develop a test for the global homogeneity of conditional potential outcome distributions that accommodates discrepancies beyond the maximum mean discrepancy (MMD), has provably valid type 1 error, and is consistent against fixed alternatives -- the first test, to our knowledge, with such guarantees in this setting. Furthermore, we derive exact closed-form expressions for two natural discrepancies (including the MMD), and provide a computationally efficient, permutation-free algorithm for our test.

翻译：除了条件平均处理效应之外，处理还可能以协变量依赖的方式影响整个结果分布，例如改变特定亚群的方差或尾部风险。我们提出了一种新的估计量来捕捉此类条件分布处理效应，并开发了一种在局部渐近意义上达到极小极大最优的双重稳健估计器。基于此，我们构建了一种检验方法，用于检验条件潜在结果分布的全局同质性；该方法不仅适用于最大均值差异（MMD）之外的差异度量，且具有可证明有效的第一类错误控制能力，并对固定备择假设具有一致性——据我们所知，这是该领域首个具备此类理论保证的检验方法。此外，我们推导了两种自然差异度量（包括MMD）的精确闭式表达式，并为该检验提供了一种无需置换、计算高效的算法。