我们在存在干扰的观测性设置下,研究从单个网络中估计平均处理效应(ATE)。弱跨单元依赖性通过一个内生的同伴效应(即网络自回归)项建模,该效应引发随网络距离衰减的依赖性,从而将常见的有限阶干扰条件放宽至无限阶干扰。我们提出一种目标最小损失估计(TMLE)程序,以消除初始估计量的插件偏差。在目标化步骤中,所生成的调整方向融入了网络自回归结构,并为各单元分配异质的、依赖于网络结构的权重。我们发现,与协变量 $\mathbf{X}_i$ 相关的渐近主导项可表示为一个 $V$-统计量,其阶数随网络度数发散。为此类复杂网络依赖场景,我们发展了一种新颖的极限理论,以建立渐近正态性。当 $\mathbf{X}_i$ 独立同分布生成且使用经验分布进行估计时,我们证明所提方法可实现比现有方法更小的渐近方差,并为方差估计提供了理论保证。本文通过大量数值模拟及一场直播数据实证分析,展示了所提方法的优势。
We study estimation of the average treatment effect (ATE) from a single network in observational settings with interference. The weak cross-unit dependence is modeled via an endogenous peer-effect (network autoregressive) term that induces distance-decaying network dependence, relaxing the common finite-order interference to infinite interference. We propose a targeted minimum loss estimation (TMLE) procedure that removes plug-in bias from an initial estimator. The targeting step yields an adjustment direction that incorporates the network autoregressive structure and assigns heterogeneous, network-dependent weights to units. We find that the asymptotic leading term related to the covariates $\mathbf{X}_i$ can be formulated into a $V$-statistic whose order diverges with the network degrees. A novel limit theory is developed to establish the asymptotic normality under such complex network dependent scenarios. We show that our method can achieve smaller asymptotic variance than existing methods when $\mathbf{X}_i$ is i.i.d. generated and estimated with empirical distribution, and provide theoretical guarantees for estimating the variance. Extensive numerical studies and a live-streaming data analysis are presented to illustrate the advantages of the proposed method.