We consider a potential outcomes model in which interference may be present between any two units but the extent of interference diminishes with spatial distance. The causal estimand is the global average treatment effect, which compares outcomes under the counterfactuals that all or no units are treated. We study a class of designs in which space is partitioned into clusters that are randomized into treatment and control. For each design, we estimate the treatment effect using a Horvitz-Thompson estimator that compares the average outcomes of units with all or no neighbors treated, where the neighborhood radius is of the same order as the cluster size dictated by the design. We derive the estimator's rate of convergence as a function of the design and degree of interference and use this to obtain estimator-design pairs that achieve near-optimal rates of convergence under relatively minimal assumptions on interference. We prove that the estimators are asymptotically normal and provide a variance estimator. For practical implementation of the designs, we suggest partitioning space using clustering algorithms.
翻译:我们考虑一个潜在结果模型,其中两个单元之间可能存在干扰,但干扰的程度会降低空间距离。因果估计效应是全球平均处理效果,将所有或没有单位得到处理的反事实下的结果进行比较。我们研究空间被分割成可随机进入处理和控制的组群的一类设计。对于每一种设计,我们使用Horvitz-Thompson估计器来估计处理效果,将单元的平均结果与所有被处理的或没有被处理的邻居进行比较,而周围半径与设计所指定的组群大小的顺序相同。我们用设计和干扰程度的函数来计算估计估计估计单位的趋同率,并以此获得在相对最低的干扰假设下达到近于最佳的趋同率的天主设计-设计对配对。我们证明估计器是正常的,并提供差异估计器。对于设计的实际实施,我们建议使用组合算法对空间进行分割。