This paper studies the efficient estimation of a large class of treatment effect parameters that arise in the analysis of experiments. Here, efficiency is understood to be with respect to a broad class of treatment assignment schemes for which the marginal probability that any unit is assigned to treatment equals a pre-specified value, e.g., one half. Importantly, we do not require that treatment status is assigned in an i.i.d. fashion, thereby accommodating complicated treatment assignment schemes that are used in practice, such as stratified block randomization and matched pairs. The class of parameters considered are those that can be expressed as the solution to a restriction on the expectation of a known function of the observed data, including possibly the pre-specified value for the marginal probability of treatment assignment. We show that this class of parameters includes, among other things, average treatment effects, quantile treatment effects, local average treatment effects as well as the counterparts to these quantities in experiments in which the unit is itself a cluster. In this setting, we establish two results. First, we derive a lower bound on the asymptotic variance of estimators of the parameter of interest in the form of a convolution theorem. Second, we show that the n\"aive method of moments estimator achieves this bound on the asymptotic variance quite generally if treatment is assigned using a "finely stratified" design. By a "finely stratified" design, we mean experiments in which units are divided into groups of a fixed size and a proportion within each group is assigned to treatment uniformly at random so that it respects the restriction on the marginal probability of treatment assignment. In this sense, "finely stratified" experiments lead to efficient estimators of treatment effect parameters "by design" rather than through ex post covariate adjustment.

翻译：本文研究实验分析中一大类处理效应参数的有效估计问题。这里的“有效性”是针对一类广泛的处理分配方案而言的，这些方案要求任何单元被分配至处理组的边际概率等于预设值（如二分之一）。重要的是，我们并不要求处理状态以独立同分布的方式分配，从而能够容纳实践中使用的复杂处理分配方案，例如分层区组随机化和配对设计。所考虑的参数类别是那些可以表示为对观测数据已知函数期望施加约束的解，其中可能包括处理分配边际概率的预设值。我们证明，该参数类别涵盖（除其他外）平均处理效应、分位数处理效应、局部平均处理效应，以及当单元本身为集群时这些量的对应形式。在此框架下，我们建立两个结果。首先，我们通过卷积定理形式推导出感兴趣参数估计量渐近方差的下界。其次，我们证明，若采用“精细分层”设计分配处理，则朴素矩法估计量能在相当普遍的情况下达到该渐近方差下界。所谓“精细分层”设计，是指将单元分为固定大小的组，每组内按均匀随机方式分配一定比例至处理组，从而满足对处理分配边际概率的约束。在此意义上，“精细分层”实验通过“设计本身”而非事后协变量调整，实现了处理效应参数的有效估计。