AI 中文总结
本文针对网络实验的干扰场景，提出基于设计的极小极大风险理论，推导了极小极大率的上下界，并将其应用于直接处理效应和全局平均处理效应的分析。
AI 中文摘要
网络实验被广泛应用于社会科学与医学科学中，以研究存在干扰情况下的因果效应。尽管已有大量研究开发了改进的统计方法，但这些场景下统计估计的基本极限仍未被充分理解。本文针对任意邻域干扰模型下的网络实验，开发并研究了一种基于设计的极小极大风险理论。该极小极大风险概念描述了所有统计方法在观测干扰网络上研究特定因果效应时的最优精度。研究表明，极小极大风险是对应冲突图的函数，该冲突图捕捉了在给定观测干扰情况下，与估计量相关的潜在结果的固有不可观测性。本文的主要贡献是针对极小极大率的一系列上界和下界，这些界是基于冲突图的局部和全局连通性性质得到的。为说明其效用，将这些一般结果应用于两种常用效应的极小极大分析：直接处理效应和全局平均处理效应。
英文摘要
Network experiments are used throughout the social and medical sciences to investigate causal effects under the presence of interference. While a large body of work has developed improved statistical procedures, the fundamental limits of statistical estimation in these settings is less well understood. In this paper, we develop and investigate a design-based theory of minimax risk for network experiments under an arbitrary neighborhood interference model. Our notion of minimax risk describes the optimal precision among all statistical procedures for investigating a particular causal effect on the observed interference network. We show that the minimax risk is a function of the corresponding conflict graph, which captures inherent unobservability of estimand-relevant potential outcomes given the observed interference network. Our main contribution is a series of upper and lower bounds on the minimax rate in terms of local and global connectivity properties of the conflict graph. To illustrate their utility, we apply these general results to obtain minimax analyses for two commonly studied effects: the direct treatment effect and global average treatment effect.
