Researchers often use linear regression to analyse randomized experiments to improve treatment effect estimation by adjusting for imbalances of covariates in the treatment and control groups. Our work offers a randomization-based inference framework for regression adjustment in stratified randomized experiments. Under mild conditions, we re-establish the finite population central limit theorem for a stratified experiment. We prove that both the stratified difference-in-means and the regression-adjusted average treatment effect estimators are consistent and asymptotically normal. The asymptotic variance of the latter is no greater and is typically lesser than that of the former. We also provide conservative variance estimators to construct large-sample confidence intervals for the average treatment effect.

中文翻译：

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分层随机实验中回归调整的平均治疗效果估计

研究人员经常使用线性回归来分析随机实验，通过调整治疗组和对照组协变量的不平衡来改进治疗效果估计。我们的工作为分层随机实验中的回归调整提供了一个基于随机化的推理框架。在温和条件下，我们重新建立了分层实验的有限总体中心极限定理。我们证明分层均值差异和回归调整的平均治疗效果估计量是一致的且渐近正态。后者的渐近方差不大于前者，通常小于前者。我们还提供了保守方差估计器来构建平均治疗效果的大样本置信区间。