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Abstract:
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Randomization is a basis for the statistical inference of treatment effects without strong assumptions on the outcome-generating process. Appropriately using covariates further yields more precise estimators in randomized experiments. R. A. Fisher suggested blocking on discrete covariates in the design stage or conducting the analysis of covariance (ANCOVA) in the analysis stage. In fact, we can embed blocking into a wider class of experimental design called reran- domization, and extend the classical ANCOVA to more general regression-adjusted estimators. Rerandomization trumps complete randomization in the design stage, and regression adjust- ment trumps the simple difference-in-means estimator in the analysis stage. It is then intuitive to use both rerandomization and regression adjustment. Under the randomization-inference framework, we establish a unified theory allowing the designer and analyzer to have access to different sets of covariates. We find that asymptotically (a) for any given estimator with or with- out regression adjustment, using rerandomization will never hurt either the sampling precision or the estimated precision, and (b) for any given design with or without
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