Regression adjustment is widely used for the analysis of randomized experiments to improve the estimation efficiency of the treatment effect. This paper reexamines a weighted regression adjustment method termed as tyranny-of-the-minority (ToM), wherein units in the minority group are given greater weights. We demonstrate that the ToM regression adjustment is more robust than Lin 2013's regression adjustment with treatment-covariate interactions, even though these two regression adjustment methods are asymptotically equivalent in completely randomized experiments. Moreover, we extend ToM regression adjustment to stratified randomized experiments, completely randomized survey experiments, and cluster randomized experiments. We obtain design-based properties of the ToM regression-adjusted average treatment effect estimator under such designs. In particular, we show that ToM regression-adjusted estimator improves the asymptotic estimation efficiency compared to the unadjusted estimator even when the regression model is misspecified, and is optimal in the class of linearly adjusted estimators. We also study the asymptotic properties of various heteroscedasticity-robust standard error estimators and provide recommendations for practitioners. Simulation studies and real data analysis demonstrate ToM regression adjustment's superiority over existing methods.
翻译:重新回归调整被广泛用于分析随机实验,以提高治疗效果的估计效率。本文件重新审查了一种称为“少数暴政”(ToM)的加权回归调整方法,其中对少数群体中的单位给予更大的加权权重。我们证明,尽管这两种回归调整方法在完全随机化的实验中都与完全随机化的实验中与上述两种回归调整方法相仿。此外,我们还将 ToM回归调整调整扩大到分层随机化实验、完全随机化的调查实验和分组随机化实验。我们在这种设计下获得了基于设计设计的“TOM回归调整平均处理效果估计仪”的设计属性,其中对少数群体中的单位给予更大的加权权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权重权。。