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20161216 Asymptotic Theory of Rerandomization in Treatment-Control Experiments

时间：2016-12-14

时间:12月16日周五晚6：00-7:00

地点:明德主楼1030

报告人:丁鹏 (Department of Statistics，UC
Berkeley)

Title:

Asymptotic Theory of Rerandomization in Treatment-Control Experiments

Abstract:

Although complete randomization ensures
covariate balance on average, the chance for 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. To supplement
existing results, 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 a truncated Gaussian random variable. This distribution follows because
rerandomization affects only the projection of potential outcomes onto the
covariate space but does not affect the corresponding orthogonal residuals. Our
work allows the construction of accurate large-sample confidence intervals for
the average causal effect, thereby revealing further advantages of
rerandomization over complete randomization.

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