Post-stratification is often used to estimate treatment effects with higher efficiency. However, most of the 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：后分层常用于以更高效率估计处理效应。然而，现有大多数后分层框架依赖于协变量分布的先验知识，并假设单元被无误地划分到后分层中。我们提出了一种新方法，通过使用预测回归模型将协变量映射到后分层因子（PSF），以确定合理的分层规则。受自举聚合（bagging）方法启发，我们利用袋外删除-D折刀法来估计分层边界、分层权重以及点估计的方差。基于这些估计量构建置信区间，以考虑来自分层边界和权重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，我们所提出的方法能持续提升估计效率，并且比回归插补方法更为稳健。