Asymptotic theory of rerandomization in treatment-control experiments

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 cr...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS Vol. 115; no. 37; p. 9157
Main Authors: Li, Xinran, Ding, Peng, Rubin, Donald B
Format: Journal Article
Language:English
Published: United States 11.09.2018
Subjects:
Models, Theoretical
Random Allocation
quantile range
causal inference
geometry of rerandomization
Mahalanobis distance
covariate balance
ISSN:1091-6490, 1091-6490
Online Access:Get more information
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Summary: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 asymptotic quantile ranges of the difference-in-means estimator. Moreover, our work constructs accurate large-sample confidence intervals for the average causal effect.
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ISSN:1091-6490
1091-6490
DOI:10.1073/pnas.1808191115