AI 中文总结
该研究为集群实验中干扰下的基于设计的因果推断开发通用框架，刻画线性加权估计量，给出新估计量，建立中心极限定理和保守方差估计量，通过模拟提供实用指导。
AI 中文摘要
我们为通过两阶段随机化在相互连接的单元网络上进行的集群实验中干扰下基于设计的因果推断开发了一个通用框架，无需依赖暴露映射假设、排除跨集群干扰或伯努利处理分配。在此框架内，我们建立了由Godambe（1955）定义的线性加权估计量（LW）的完整刻画，其实现了干扰下各种网络因果效应的识别。这个一般类包括几个新的估计量，相对于现有方法如标准逆概率处理加权，具有改进的理论保证和优越的有限样本性能。对于这个类中的大多数估计量，我们建立了中心极限定理和保守方差估计量，这使我们能够描述不同加权方案可能表现出的不同渐近行为。特别是，我们研究了集群级别的随机化如何影响各种估计量的渐近行为，并确定了一类与集群无关的LW估计量，其收敛速度与集群数量无关，达到最优根N速度，其中N表示单元总数。值得注意的是，对于完全随机化，我们开发了可能具有独立意义的新技术，既用于建立一般相关统计量之和的中心极限定理，又用于构造保守和偏差校正的方差估计量。我们用广泛的模拟研究补充我们的理论结果，这些研究为在广泛的干扰结构下选择加权方法和实验设计提供了实用指导。
英文摘要
We develop a general framework for design-based causal inference under interference in cluster experiments conducted via two-stage randomization on a network of interconnected units, without relying on exposure mapping assumptions, exclusion of cross-cluster interference, or Bernoulli treatment assignments. Within this framework, we establish a complete characterization of linear weighted estimators (LW) as defined by Godambe (1955) that achieve identification of various network causal effects under interference. This general class includes several new estimators with improved theoretical guarantees and superior finite-sample performance relative to existing approaches such as standard inverse-probability-of-treatment weighting. For most estimators in this class, we establish central limit theorems and conservative variance estimators, which allows us to describe the distinct asymptotic behavior exhibited by different weighting schemes potentially of interest. In particular, we study how randomization at the cluster-level affects the asymptotic behavior of various estimators, and we identify a subclass of cluster-agnostic LW estimators whose convergence rates are independent of the number of clusters and attain the optimal root-N rate, where N denotes the total number of units. Notably, for complete randomization we develop new techniques that may be of independent interest, both to establish a central limit theorem for sums of general dependent statistics and to construct conservative and bias-corrected variance estimators. We complement our theoretical results with extensive simulation studies that offer practical guidance on the choice of weighting method and experimental design under a wide range of interference structures.
