Efficient Treatment Effect Estimation with Out-of-bag Post-stratification

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.