Asymptotic inference of causal effects with observational studies trimmed by the estimated propensity scores
针对倾向得分接近0或1时重叠假设被违反的问题，提出一种平滑加权方法近似样本修剪，具有渐近线性性，允许使用自助法对目标总体进行推断，并扩展到处理组的平均处理效应。
Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores close to |$0$| or |$1$|, so both practical and theoretical researchers suggest dropping units with extreme estimated propensity scores. However, existing trimming methods often do not incorporate the uncertainty in this design stage and restrict inference to only the trimmed sample, due to the nonsmoothness of the trimming. We propose a smooth weighting, which approximates sample trimming and has better asymptotic properties. An advantage of our estimator is its asymptotic linearity, which ensures that the bootstrap can be used to make inference for the target population, incorporating uncertainty arising from both design and analysis stages. We extend the theory to the average treatment effect on the treated, suggesting trimming samples with estimated propensity scores close to |$1$|.