拓展因果效应分析，引入分布特征与变量关系的统计量。
Moments of Causal Effects
- 定义因果效应的各阶矩与协变矩，刻画其分布形态
- 给出有限样本下矩估计方法，并在真实医疗数据中验证
- 适合关注因果推断分布特性的研究人员
随机变量的矩是描述概率分布形状的基础统计量，包括均值、方差、偏度和峰度等；而乘积矩（如协方差、相关系数）则揭示多变量间的关联。传统因果推断主要关注平均因果效应，本文首次提出因果效应各阶矩及乘积矩的定义、可识别性定理与边界估计，用于分析因果效应的分布特征及其相互关系。通过实验展示了从有限样本中估计这些矩的方法，并在真实医疗数据集上验证了其实际应用价值。
原文摘要 · Abstract (English)
The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments, including covariance and correlation, reveal the relationships between multiple random variables. On the other hand, the primary focus of causal inference is the evaluation of causal effects, which are defined as the difference between two potential outcomes. While traditional causal effect assessment focuses on the average causal effect, this work provides definitions, identification theorems, and bounds for moments and product moments of causal effects to analyze their distribution and relationships. We conduct experiments to illustrate the estimation of the moments of causal effects from finite samples and demonstrate their practical application using a real-world medical dataset.
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