用于精细分层实验的图拉普拉斯方差估计器
Graph-Laplacian Variance Estimators for Finely Stratified Experiments
AI总结：
本文针对精细分层实验，提出度校准图拉普拉斯方差估计器，推导其偏差性质，提出正则化图估计器以权衡局部性与最坏情况偏差，通过模拟验证相关结论。
AI中文摘要：
本文研究精细分层实验中基于设计的平均处理效应推断，其中不确定性仅源于随机处理分配。我们关注的场景是：首先根据基线协变量将单元分层为固定大小的组，随后在每个组内恰好分配一个单元接受处理。在此设定下，我们引入一类图拉普拉斯方差估计器，其中分层构成加权图的顶点，边权重决定如何聚合层间比较。Imai（2008）的经典估计器对应于完全图，其边权重经归一化使得每个分层的加权度为1；而配对分层估计器则源自完美匹配图。对于每个顶点加权度为1的度校准图子类，我们推导得到精确偏差恒等式，表明对应估计器存在向上偏差，偏差由相邻分层间真实分层水平处理效应的平方差决定。因此，此类估计器均可用于有效推断。该恒等式进一步表明，当处理效应随协变量平滑变化时，基于协变量完美匹配构造的配对分层估计器可产生较小偏差。然而，若不存在此类平滑性，我们证明配对分层估计器可呈现较大的最坏情况偏差，且在度校准估计器类中，完全图估计器在处理效应异质性的弱约束下，对归一化偏差而言是极小极大最优的。受此对比启发，我们提出一种正则化图估计器，其可控制最坏情况归一化偏差，同时保留配对分层估计器的大部分局部性。模拟结果说明了局部性与最坏情况保护之间的权衡。
英文摘要：
This paper considers design-based inference on the average treatment effect in finely stratified experiments, where uncertainty arises only from the randomized treatment assignment. We focus on settings in which units are first stratified into groups of fixed size according to baseline covariates and, then within each group, exactly one unit is assigned to treatment. In this setting, we introduce a class of graph-Laplacian variance estimators in which strata form the vertices of a weighted graph and edge weights determine how between-stratum comparisons are aggregated. The canonical estimator of Imai (2008) corresponds to a complete graph with edge weights normalized so that each stratum has weighted degree one, while a paired-stratum estimator arises from a perfect matching graph. For the subclass of degree-calibrated graphs, in which each vertex has weighted degree one, we derive an exact bias identity showing that the corresponding estimators are upward-biased, with bias governed by squared differences in the true stratum-level treatment effects across adjacent strata. As a result, any such estimator may be used for valid inference. The identity further suggests that paired-stratum estimators constructed from a covariate-based perfect matching can induce small biases when treatment effects vary smoothly with the covariates. Without such smoothness, however, we show that paired-stratum estimators can exhibit large worst-case bias, and that, within the class of degree-calibrated estimators, the complete-graph estimator is minimax optimal for normalized bias under a weak bound on treatment-effect heterogeneity. Motivated by this contrast, we propose a regularized graph estimator that controls worst-case normalized bias while preserving much of the locality of the paired-stratum estimator. Simulations illustrate the resulting tradeoff between locality and worst-case protection.
