In this paper, we propose to use sufficient dimension reduction (SDR) in conjunction with nonparametric techniques to estimate the average treatment effect on the treated (ATT), a parameter of common interest in causal inference. The proposed method is applicable under a general low‐dimensional structure in the data, and avoids both the risk of model misspecification and the “curse of dimensionality,” for which it often outperforms the existing parametric and nonparametric methods. We develop the theoretical properties of the proposed method, including its asymptotic normality, its asymptotic super‐efficiency, and its equivalent form as an augmented inverse probability weighting estimator. We also consider the impact of SDR estimation in the asymptotic studies. These theoretical results are further illustrated by the simulation studies at the end.

中文翻译：

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通过充分减小尺寸来估计对被处理物的平均处理效果

在本文中，我们建议结合充分的降维（SDR）和非参数技术来估计对已处理（ATT）的平均处理效果，这是因果推理中常用的参数。所提出的方法适用于数据中的一般低维结构，并且避免了模型错误指定的风险和“维数的诅咒”，因为它们通常优于现有的参数和非参数方法。我们开发了该方法的理论特性，包括其渐近正态性，其渐近超高效性以及与之等效的形式，作为增强的逆概率加权估计器。我们还考虑了渐进研究中SDR估算的影响。最后的仿真研究进一步说明了这些理论结果。