We consider estimation and inference on average treatment effects under unconfoundedness conditional on the realizations of the treatment variable and covariates. Given nonparametric smoothness and/or shape restrictions on the conditional mean of the outcome variable, we derive estimators and confidence intervals (CIs) that are optimal in finite samples when the regression errors are normal with known variance. In contrast to conventional CIs, our CIs use a larger critical value that explicitly takes into account the potential bias of the estimator. When the error distribution is unknown, feasible versions of our CIs are valid asymptotically, even when ‐inference is not possible due to lack of overlap, or low smoothness of the conditional mean. We also derive the minimum smoothness conditions on the conditional mean that are necessary for ‐inference. When the conditional mean is restricted to be Lipschitz with a large enough bound on the Lipschitz constant, the optimal estimator reduces to a matching estimator with the number of matches set to one. We illustrate our methods in an application to the National Supported Work Demonstration.

中文翻译：

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无混杂条件下有限样本最优估计和平均治疗效果的推论

我们考虑在无混淆的情况下对平均治疗效果的估计和推论，条件是治疗变量和协变量的实现。给定非参数平滑度和/或形状变量对结果变量的条件均值的限制，当回归误差为正常且已知方差时，我们得出在有限样本中最佳的估计量和置信区间（CIs）。与常规配置项相比，我们的配置项使用较大的临界值，该临界值明确考虑了估计量的潜在偏差。当错误分布未知时，即使在以下情况下，CI的可行版本也将渐近有效-由于没有重叠或条件均值的低平滑性，因此无法进行推断。我们还根据条件均值得出了推论所需的最小平滑度条件。当条件均值限制为Lipschitz且Lipschitz常数的边界足够大时，最佳估计量将减少为匹配次数为1的匹配估计量。我们在“国家支持的工作演示”的应用程序中说明了我们的方法。