连续处理因果导数效应的双重稳健推断
Doubly Robust Inference on Causal Derivative Effects for Continuous Treatments
AI总结：
针对连续处理，研究存在和不存在positivity条件下剂量反应曲线导数的非参数推断，提出双重稳健估计量，解决传统方法不足，通过模拟和案例验证其适用性与效率。
摘要：
针对连续处理的因果推断统计方法主要聚焦于估计平均潜在结果函数，即通常所说的剂量反应曲线。然而，指示处理效应的往往不是剂量反应曲线本身，而是其导数函数。本文研究了存在和不存在 positivity 条件下剂量反应曲线导数的非参数推断。在 positivity 条件及其他正则条件下，我们提出一种基于核平滑的双重稳健（DR）推断方法来估计剂量反应曲线的导数。当 positivity 条件不满足时，我们证明了传统逆概率加权（IPW）和 DR 估计量的不一致性，并引入新的偏差校正 IPW 和 DR 估计量。在所有设定中，我们的 DR 估计量达到标准非参数收敛速率下的渐近正态性，并具有非参数效率保证。此外，我们的方法揭示了其与非参数支撑和水平集估计问题的有趣联系。最后，我们通过模拟和评估一项职业培训项目的案例研究，证明了所提出估计量的适用性。
英文摘要：
Statistical methods for causal inference with continuous treatments mainly focus on estimating the mean potential outcome function, commonly known as the dose-response curve. However, it is often not the dose-response curve but its derivative function that signals the treatment effect. In this paper, we investigate nonparametric inference on the derivative of the dose-response curve with and without the positivity condition. Under the positivity and other regularity conditions, we propose a doubly robust (DR) inference method for estimating the derivative of the dose-response curve using kernel smoothing. When the positivity condition is violated, we demonstrate the inconsistency of conventional inverse probability weighting (IPW) and DR estimators, and introduce novel bias-corrected IPW and DR estimators. In all settings, our DR estimator achieves asymptotic normality at the standard nonparametric rate of convergence with nonparametric efficiency guarantees. Additionally, our approach reveals an interesting connection to nonparametric support and level set estimation problems. Finally, we demonstrate the applicability of our proposed estimators through simulations and a case study of evaluating a job training program.
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