Heavy Tail Robust Estimation and Inference for Average Treatment Effects
平均处理效应的厚尾稳健估计与推断AI 解读 ↓
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平均处理效应的厚尾稳健估计与推断
- 研究问题
- 在条件无混杂但处理组与对照组重叠有限时，如何应对逆概率加权变量的厚尾及慢收敛，并减少修剪引入的偏差？
- 方法与思路
- 作者将参数化倾向得分估计代入识别 ATE 的加权变量，按该变量的极端值自适应尾部修剪，并估计和消除相应偏差。
- 材料陈述的贡献
- 摘要称该方法避免按协变量或倾向得分修剪的部分问题；模拟中仅去除少量极端值即可获得低偏差、低均方误差及近似正态表现。
- 阅读关注点
- 应核对倾向得分模型与尾部条件、修剪比例的选择、非对称无限方差下的偏差修正，以及收敛率和推断结论的适用范围。
- 阅读边界
- 所给版本为 arXiv 预印本，不能据此认定已同行评审或获期刊接收；摘要未给出尾部参数、修剪规则及模拟数值，不能据此认定普遍优于其他方法。
原文摘要
We study the probability tail properties of Inverse Probability Weighting (IPW) estimators of the Average Treatment Effect (ATE) when there is limited overlap between the covariate distributions of the treatment and control groups. Under unconfoundedness of treatment assignment conditional on covariates, such limited overlap is manifested in the propensity score for certain units being very close (but not equal) to 0 or 1. This renders IPW estimators possibly heavy tailed, and with a slower than sqrt(n) rate of convergence. Trimming or truncation is ultimately based on the covariates, ignoring important information about the inverse probability weighted random variable Z that identifies ATE by E[Z]= ATE. We propose a tail-trimmed IPW estimator whose performance is robust to limited overlap. In terms of the propensity score, which is generally unknown, we plug-in its parametric estimator in the infeasible Z, and then negligibly trim the resulting feasible Z adaptively by its large values. Trimming leads to bias if Z has an asymmetric distribution and an infinite variance, hence we estimate and remove the bias using important improvements on existing theory and methods. Our estimator sidesteps dimensionality, bias and poor correspondence properties associated with trimming by the covariates or propensity score. Monte Carlo experiments demonstrate that trimming by the covariates or the propensity score requires the removal of a substantial portion of the sample to render a low bias and close to normal estimator, while our estimator has low bias and mean-squared error, and is close to normal, based on the removal of very few sample extremes.