  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.
