Simultaneous Inference for Proximal Causal Learning with Weak Proxies
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弱代理变量下近端因果学习的同时推断
- 研究问题
- 处理与结果代理变量较弱时，如何为边际反事实分布和分位数处理效应构造有效的同时置信带，并控制桥估计偏差？
- 方法与思路
- 作者定义弱代理强度，收紧总体偏差界，建立跨处理和阈值的统一展开，再通过分布置信带反演构造分位数效应带。
- 材料陈述的贡献
- 摘要称新界减少对代理强度倒数的依赖，临界值在桥估计后仍有效，方法无需密度估计，并报告模拟覆盖改善。
- 阅读关注点
- 应核对桥函数识别、弱代理强度衰减限制，以及统一展开、临界值有效性和置信带反演分别需要的条件。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要数值属于特定模拟，未提供完整条件，不能保证一般弱代理下有效。
原文摘要
Proximal causal learning uses the treatment-inducing proxy and the outcome-inducing proxy through the outcome bridge and the treatment bridge to provide a way to address unobserved confounding in observational studies. This paper studies simultaneous inference for the marginal counterfactual distribution and quantile treatment effect under weak proxies. First, we propose a measure of weak-proxy strength and tightens the population-bias bound for the counterfactual CDF estimate. The baseline Cauchy--Schwarz bound introduces the inverse of weak-proxy strength twice, whereas the proposed bound introduces the inverse of weak-proxy strength only once and is sharp for the bridge estimators, thereby relaxing the restriction on the decay rate of weak-proxy strength. Second, we prove that, even when outcome thresholds vary continuously, the number of distinct estimated outcome bridges is at most one greater than the number of observations in the training sample, thereby establishing a uniform expansion across treatment arms and outcome thresholds. Finally, we prove that the critical value remains valid after bridge estimation, thereby obtaining simultaneous CDF bands, and constructs quantile treatment effect bands through confidence-band inversion. The proposed method provides deterministic band-width bounds and does not require counterfactual density estimation. In the numerical study, the baseline Cauchy--Schwarz bound overestimates the true population bias by a factor of approximately 50, whereas the proposed bound is very close to the true population bias. The quantile treatment effect bands constructed by the proposed method achieve coverage of 99.8\%--100.0\% while being only approximately 20\% wider than the oracle 95\% bands, compared with baseline coverage of 68.4\%--89.2\%.