Abstract A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in which high-dimensional covariates are present and revisits the standard assumptions made in causal inference. We show that by employing a flexible Gaussian process framework, the assumption of strict overlap leads to very restrictive assumptions about the distribution of covariates, results for which can be characterized using classical results from Gaussian random measures as well as reproducing kernel Hilbert space theory. In addition, we propose a strategy for data-adaptive causal effect estimation that does not rely on the strict overlap assumption. These findings reveal under a focused framework the stringency that accompanies the use of the treatment positivity assumption in high-dimensional settings.

中文翻译：

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高维协变量重叠和因果效应估计的高斯过程框架

摘要 分析非随机观察性研究的一个强大工具是潜在结果模型。利用该框架，分析师可以估计平均治疗效果。本文考虑了存在高维协变量的情况，并重新审视了因果推断中的标准假设。我们表明，通过采用灵活的高斯过程框架，严格重叠的假设导致对协变量分布的非常严格的假设，其结果可以使用高斯随机测度的经典结果以及再现核希尔伯特空间理论来表征。此外，我们提出了一种不依赖于严格重叠假设的数据自适应因果效应估计策略。