Post-stratification is often used to estimate treatment effects with higher efficiency. However, the majority of existing post-stratification frameworks depend on prior knowledge of the distributions of covariates and assume that the units are classified into post-strata without error. We propose a novel method to determine a proper stratification rule by mapping the covariates into a post-stratification factor (PSF) using predictive regression models. Inspired by the bootstrap aggregating (bagging) method, we utilize the out-of-bag delete-D jackknife to estimate strata boundaries, strata weights, and the variance of the point estimate. Confidence intervals are constructed with these estimators to take into account the additional variability coming from uncertainty in the strata boundaries and weights. Extensive simulations show that our proposed method consistently improves the efficiency of the estimates when the regression models are predictive and tends to be more robust than the regression imputation method.

翻译：事后分层常用于提高处理效应估计的效率。然而，现有的大多数事后分层框架依赖于协变量分布的先验知识，并假设单元被无误差地划分到事后层中。我们提出了一种新方法，通过使用预测性回归模型将协变量映射为事后分层因子（PSF），从而确定合理的分层规则。受自助聚合（bagging）方法的启发，我们利用袋外删除-D折刀法来估计层边界、层权重以及点估计的方差。基于这些估计量构建置信区间，以考虑来自层边界和层不确定性的额外变异性。大量模拟表明，当回归模型具有预测性时，所提出的方法能持续提高估计效率，并且通常比回归插补法更为稳健。