Causal inference on distribution functions
针对结果变量为累积分布函数（非线性空间）的情形，提出因果效应的新框架，开发双重稳健估计量并给出渐近理论，用婚姻对体力活动模式的因果效应做示例。
Abstract Understanding causal relationships is one of the most important goals of modern science. So far, the causal inference literature has focused almost exclusively on outcomes coming from the Euclidean space Rp. However, it is increasingly common that complex datasets are best summarized as data points in nonlinear spaces. In this paper, we present a novel framework of causal effects for outcomes from the Wasserstein space of cumulative distribution functions, which in contrast to the Euclidean space, is nonlinear. We develop doubly robust estimators and associated asymptotic theory for these causal effects. As an illustration, we use our framework to quantify the causal effect of marriage on physical activity patterns using wearable device data collected through the National Health and Nutrition Examination Survey.