Heavy tail robust estimation and inference for average treatment effects
研究了处理组与对照组协变量分布重叠不足时，逆概率加权估计量出现重尾且收敛慢的问题，提出一种基于尾部修剪的稳健估计方法，通过自适应修剪大值并校正偏差，在少量样本修剪下实现低偏和近似正态性。
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 n rate of convergence. Historically estimators are either based on the assumption of strict overlap, i.e., the propensity score is bounded away from 0 and 1; or they truncate the propensity score; or trim observations based on a variety of techniques based on covariate or propensity score values. 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.