Nonparametric Estimation of Local Treatment Effects with Continuous Instruments
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连续工具变量下局部处理效应的非参数估计
- 研究问题
- 连续工具变量下，如何减少参数化限制，估计最大服从者群体的处理效应及局部工具变量曲线，并开展有效推断？
- 方法与思路
- 作者在单调性假设下定义最大服从者效应，联系剂量反应函数及其导数，提出双重稳健估计、带宽选择和方差估计程序。
- 材料陈述的贡献
- 摘要称建立了收敛速度及渐近正态性的条件，并以模拟和新生儿重症监护应用展示方法；具体优势幅度未说明。
- 阅读关注点
- 核对最大服从者的定义、完整工具变量识别条件，以及连续工具变量下辅助函数误差、带宽与渐近推断的关系。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实。摘要未列完整识别假设、收敛条件或婴儿死亡效应的估计结果。
原文摘要
Instrumental variable methods are widely used to address unmeasured confounding, yet much of the existing literature has focused on the binary instrument setting. Extensions to continuous instruments often impose strong parametric assumptions for identification and estimation, which can be difficult to justify and may limit their applicability in complex real-world settings. In this work, we develop theory and methods for nonparametric estimation of treatment effects with a continuous instrumental variable. We introduce an estimand that, under a monotonicity assumption, quantifies the treatment effect among the maximal complier class, generalizing the local average treatment effect framework to continuous instruments. Considering this estimand and the local instrumental variable curve, we draw connections to the dose-response function and its derivative, and propose doubly robust estimation methods. We establish convergence rates and conditions for asymptotic normality, providing valuable insights into the role of nuisance function estimation when the instrument is continuous. Additionally, we present practical procedures for bandwidth selection and variance estimation. Through extensive simulations, we demonstrate the advantages of the proposed nonparametric estimators. Finally, we apply our methods to data where excess travel time is an instrument for patients' likelihood of receiving care at specialized health care facilities. We use this instrument to estimate the effect of delivering at low-quality neonatal intensive care units (NICUs) on infant mortality.