Causal inference on distribution functions
Causal inference on distribution functions
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DOI：
10.1093/jrsssb/qkad008
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
Zhenhua Lin;Dehan Kong;Linbo Wang
中科院分区：
文献类型：
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作者：
Zhenhua Lin;Dehan Kong;Linbo Wang
理解因果关系是现代科学最重要的目标之一。到目前为止，因果推理文献几乎完全集中在欧几里得空间Rp的结果上。然而，将复杂的数据集最好地概括为非线性空间中的数据点是越来越常见的。在这篇文章中，我们提出了一个新的因果效应框架，它来自累积分布函数的瓦瑟斯坦空间，与欧几里德空间相比，它是非线性的。我们发展了这些因果效应的双重稳健估计和相关的渐近理论。作为例证，我们使用我们的框架，使用通过国家健康和营养检查调查收集的可穿戴设备数据来量化婚姻对身体活动模式的因果影响。
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.