Asymptotic theory of rerandomization in treatment-control experiments
Asymptotic theory of rerandomization in treatment-control experiments
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DOI：
10.1073/pnas.1808191115
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发表时间：
2018-09-11
影响因子：
11.1
通讯作者：
Rubin, Donald B.
中科院分区：
文献类型：
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作者：
Li, Xinran;Ding, Peng;Rubin, Donald B.
虽然完全随机化确保协变量平均平衡，但观察到治疗组和对照组协变量分布之间显著差异的机会随着协变量的增多而增加。再随机化抛弃不满足预先确定的协变量平衡标准的随机化，通常导致更好的协变量平衡和更精确的因果效应估计。先前的理论推导了在处理组大小相等、高斯协变量和结果分布或加性因果效应假设下的再随机化有限样本理论，但没有推导出平均因果效应的均值差估计量的一般抽样分布。我们在没有这些假设的情况下发展了重随机化的渐近理论，揭示了该估计量的非高斯渐近分布，即高斯随机变量和截断高斯随机变量的线性组合。之所以会出现这种分布，是因为再随机化只影响潜在结果在协变量空间上的投影，而不影响相应的正交残差。我们证明，与完全随机化相比，再随机化减小了均值差估计量的渐近分位数范围。此外，我们的工作为平均因果效应构建了准确的大样本置信区间。
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.