Asymptotic Theory of the Best-Choice Rerandomization using the Mahalanobis Distance
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基于马氏距离的最优选择再随机化渐近理论
- 研究问题
- 在多次随机分配中选择协变量最平衡的一次时，处理效应估计与区间推断如何变化，尤其当协变量和尝试次数随样本增长？
- 方法与思路
- 作者用马氏距离衡量平衡，研究最优选择再随机化下均值差估计量的大样本分布，并允许协变量数与随机化次数增长。
- 材料陈述的贡献
- 摘要称再随机化使渐近分布更集中、置信区间更短，并在协变量数量适中及尝试次数多项式增长的条件下达到理想精度。
- 阅读关注点
- 应核对协变量数量与尝试次数的增长限制、渐近近似和区间覆盖条件，以及所谓理想精度所对应的基准与适用情形。
- 阅读边界
- 所给版本为 arXiv 预印本，不能据此确认同行评审或期刊接收；摘要未给出增长条件和区间公式，精度结论不能任意外推。
原文摘要
Rerandomization, a design that utilizes pretreatment covariates and improves their balance between different treatment groups, has received attention recently in both theory and practice. From a survey by Bruhn and McKenzie (2009), there are at least two types of rerandomization that are used in practice: the first rerandomizes the treatment assignment until covariate imbalance is below a prespecified threshold; the second randomizes the treatment assignment multiple times and chooses the one with the best covariate balance. In this paper we will consider the second type of rerandomization, namely the best-choice rerandomization, whose theory and inference are still lacking in the literature. In particular, we will focus on the best-choice rerandomization that uses the Mahalanobis distance to measure covariate imbalance, which is one of the most commonly used imbalance measure for multivariate covariates and is invariant to affine transformations of covariates. We will study the large-sample repeatedly sampling properties of the best-choice rerandomization, allowing both the number of covariates and the number of tried complete randomizations to increase with the sample size. We show that the asymptotic distribution of the difference-in-means estimator is more concentrated around the true average treatment effect under rerandomization than under the complete randomization, and propose large-sample accurate confidence intervals for rerandomization that are shorter than that for the completely randomized experiment. We further demonstrate that, with moderate number of covariates and with the number of tried randomizations increasing polynomially with the sample size, the best-choice rerandomization can achieve the ideally optimal precision that one can expect even with perfectly balanced covariates. The developed theory and methods are also illustrated using real field experiments.