Rerandomization with Diminishing Covariate Imbalance and Diverging Number of Covariates
协变量不平衡趋零且协变量数量增长时的再随机化AI 解读 ↓
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协变量不平衡趋零且协变量数量增长时的再随机化
- 研究问题
- 能否让再随机化中的协变量不平衡随样本量适当趋零，同时达到完全平衡下的理想精度、保持稳健性，并允许协变量数量增长？
- 方法与思路
- 作者对再随机化开展更精细的渐近分析，研究不平衡程度的下降速率，并进一步考察达到所述最优性所需的协变量数量条件。
- 材料陈述的贡献
- 摘要称，在适当速率和条件下，再随机化可兼顾理想最优精度与稳健性，并在渐近意义上协调随机设计和最优设计的争论。
- 阅读关注点
- 应核对接受阈值、不平衡下降速率、协变量维度及样本量之间的关系，以及稳健性、最优精度的定义和推断实施要求。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未经核实；摘要未说明具体速率及维度条件，渐近结论不能直接保证小样本表现。
原文摘要
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 realized 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 covariate 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 controversy between two philosophies for designing experiments: randomization versus optimal and thus almost deterministic designs. Existing literature argued 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 sacrificing 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 covariates, 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. The derived theory for rerandomization provides a deeper understanding of its large-sample property and can better guide its practical implementation. Furthermore, it also helps reconcile the controversy between randomized and optimal designs in an asymptotic sense.