标题： 重尾鲁棒估计与平均处理效应的推断 显示英文标题

标题： Heavy Tail Robust Estimation and Inference for Average Treatment Effects

摘要： 我们研究了当处理组和对照组的协变量分布重叠有限时，逆概率加权（IPW）估计量的尾部特性，这些估计量用于平均处理效应（ATE）的估计。在治疗分配相对于协变量无混淆性的情况下，这种有限的重叠表现为倾向得分对于某些单位非常接近（但不等于）0或1。这使得IPW估计量可能具有较重的尾部，并且收敛速度慢于sqrt(n)。修剪或截断最终基于协变量，忽略了关于通过E[Z] = ATE识别ATE的逆概率加权随机变量Z的重要信息。我们提出了一种尾部修剪的IPW估计量，其性能对有限重叠具有鲁棒性。就倾向得分而言（通常是未知的），我们在不可行的Z中插入其参数估计量，然后通过其大值对得到的可行Z进行适配性修剪。如果Z具有不对称分布和无限方差，则修剪会导致偏差，因此我们利用现有理论和方法的重要改进来估计和消除偏差。我们的估计器避免了与协变量或倾向得分相关的修剪所导致的维度、偏差和较差的对应性质问题。蒙特卡洛实验表明，基于协变量或倾向得分的修剪需要移除样本中相当大的一部分才能使估计量偏差较小且接近正态分布，而我们的估计器具有较小的偏差和均方误差，并且基于移除少量样本极值即可接近正态分布。 显示英文摘要

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.