RERANDOMIZATION WITH DIMINISHING COVARIATE IMBALANCE AND DIVERGING NUMBER OF COVARIATES

• 成果类型: Article
• 署名作者: Wang, Yuhao; Li, Xinran
• 署名单位: Tsinghua University; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2235
• 发表日期: 2022
• 页码: 3439-3465
• 关键词: CENTRAL LIMIT-THEOREMS; regression adjustments; finite population; balance; DESIGN; bootstrap

摘要

Completely randomized experiments have been the gold standard for drawing causal inference because they can balance all potential confounding on average. However, they may suffer from unbalanced covariates for real-ized treatment assignments. Rerandomization, a design that rerandomizes the treatment assignment until a prespecified covariate balance criterion is met, has recently got attention due to its easy implementation, improved covari-ate balance and more efficient inference. Researchers have then suggested to use the treatment assignments that minimize the covariate imbalance, namely the optimally balanced design. This has caused again the long-time contro-versy between two philosophies for designing experiments: randomization versus optimal, and thus almost deterministic designs. Existing literature ar-gued that rerandomization with overly balanced observed covariates can lead to highly imbalanced unobserved covariates, making it vulnerable to model misspecification. On the contrary, rerandomization with properly balanced covariates can provide robust inference for treatment effects while sacrific-ing some efficiency compared to the ideally optimal design. In this paper, we show it is possible that, by making the covariate imbalance diminishing at a proper rate as the sample size increases, rerandomization can achieve its ideally optimal precision that one can expect with perfectly balanced covari-ates, while still maintaining its robustness. We further investigate conditions on the number of covariates for achieving the desired optimality. Our results rely on a more delicate asymptotic analysis for rerandomization, allowing both diminishing covariate imbalance threshold (or equivalently the accep-tance probability) and diverging number of covariates. The derived theory for rerandomization provides a deeper understanding of its large-sample prop-erty and can better guide its practical implementation. Furthermore, it also helps reconcile the controversy between randomized and optimal designs in an asymptotic sense.