Asymptotic theory of rerandomization in treatment-control experiments

Proceedings of the National Academy of Sciences of the United States of America
Xinran LiDonald B Rubin

Abstract

Although complete randomization ensures covariate balance on average, the chance of observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of causal effects. Previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive causal effects, but not for the general sampling distribution of the difference-in-means estimator for the average causal effect. We develop asymptotic theory for rerandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian random variable and truncated Gaussian random variables. This distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We demonstrate that, compared with complete randomization, rerandomization reduces the asympto...Continue Reading

References

Apr 1, 2004·Biostatistics·Robert GreevyPaul Rosenbaum
Jul 7, 2016·Proceedings of the National Academy of Sciences of the United States of America·Michael J HigginsJasjeet S Sekhon
Jan 1, 2015·Journal of the American Statistical Association·Kari Lock Morgan, Donald B Rubin

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