Abstract This article considers a Mann–Whitney test of distributional effects in a multivalued treatment. Specifically, we first show that, under the unconfoundedness condition, the counterfactual distributions are weighted averages, with weights satisfying some moment restrictions. We estimate the weights directly from those restrictions by maximizing a globally concave objective function and then construct the Mann–Whitney statistics with the estimated distributions. We show that our Mann–Whitney statistics are efficient, attaining the semiparametric efficiency bound which is also derived here. A simulation study and an application to the analysis of racial discrimination illustrate the practical value of the proposed approach.

中文翻译：

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多值处理中分布效应的 Mann-Whitney 检验

摘要 本文考虑了多值处理中分布效应的 Mann-Whitney 检验。具体来说，我们首先表明，在无混杂条件下，反事实分布是加权平均值，权重满足一些矩限制。我们通过最大化全局凹目标函数直接从这些限制中估计权重，然后用估计的分布构建 Mann-Whitney 统计。我们表明我们的 Mann-Whitney 统计是有效的，达到了半参数效率界限，这也是在这里导出的。模拟研究和种族歧视分析的应用说明了所提出方法的实用价值。