We develop new semiparametric methods for estimating treatment effects. We focus on settings where the outcome distributions may be thick tailed, where treatment effects may be small, where sample sizes are large and where assignment is completely random. This setting is of particular interest in recent online experimentation. We propose using parametric models for the treatment effects, leading to semiparametric models for the outcome distributions. We derive the semiparametric efficiency bound for the treatment effects for this setting, and propose efficient estimators. In the leading case with constant quantile treatment effects one of the proposed efficient estimators has an interesting interpretation as a weighted average of quantile treatment effects, with the weights proportional to minus the second derivative of the log of the density of the potential outcomes. Our analysis also suggests an extension of Huber's model and trimmed mean to include asymmetry.

翻译：我们开发了用于估计处理效应的新半参数方法。我们重点关注结果分布可能存在厚尾、处理效应可能较小、样本量较大且分配完全随机的情况。这一设定在近期线上实验中尤为受关注。我们提出为处理效应使用参数模型，从而得到结果分布的半参数模型。我们推导了该设定下处理效应的半参数效率界，并提出了有效估计量。在分位数处理效应为常数的典型情形中，所提出的有效估计量之一具有有趣的解释：它是分位数处理效应的加权平均，权重与潜在结果密度对数的二阶导数成比例。我们的分析还建议将Huber模型和修剪均值扩展至包含非对称情形。