标题： 在协变量自适应随机化下的平均处理效应的高效半参数估计 显示英文标题

标题： Efficient Semiparametric Estimation of Average Treatment Effects Under Covariate Adaptive Randomization

摘要： 使用协变量自适应随机化（CAR）的实验在应用经济学和其他领域中很常见。 在这样的实验中，实验者首先根据观察到的基线协变量对样本进行分层，然后在这些层内随机分配处理，以根据预定义的层特定目标分配比例实现平衡。 在本文中，我们计算了在使用二元处理的此类实验中估计平均处理效应（ATE）的半参数效率界限，允许使用Bugni、Canay和Shaikh（2018、2019）中考虑的CAR过程类别。 这是一个广泛的程序类别，其动机来自于实际中使用的程序。 层特定的目标比例在这些实验中起到了所有基线协变量条件下的倾向得分的作用（而不仅仅是层）。 因此，该效率界限是Hahn（1998）中界限的一个特例，但条件是所有基线协变量。 此外，通过使用交叉拟合的Nadaraya-Watson核估计器形成非参数回归调整，证明了在与推导该界限相同的条件下可以达到这一效率界限。 显示英文摘要

摘要： Experiments that use covariate adaptive randomization (CAR) are commonplace in applied economics and other fields. In such experiments, the experimenter first stratifies the sample according to observed baseline covariates and then assigns treatment randomly within these strata so as to achieve balance according to pre-specified stratum-specific target assignment proportions. In this paper, we compute the semiparametric efficiency bound for estimating the average treatment effect (ATE) in such experiments with binary treatments allowing for the class of CAR procedures considered in Bugni, Canay, and Shaikh (2018, 2019). This is a broad class of procedures and is motivated by those used in practice. The stratum-specific target proportions play the role of the propensity score conditional on all baseline covariates (and not just the strata) in these experiments. Thus, the efficiency bound is a special case of the bound in Hahn (1998), but conditional on all baseline covariates. Additionally, this efficiency bound is shown to be achievable under the same conditions as those used to derive the bound by using a cross-fitted Nadaraya-Watson kernel estimator to form nonparametric regression adjustments.