We study estimation and inference on causal parameters under finely stratified rerandomization designs, which use baseline covariates to match units into groups (e.g. matched pairs), then rerandomize within-group treatment assignments until a balance criterion is satisfied. We show that finely stratified rerandomization does partially linear regression adjustment "by design," providing nonparametric control over the stratified covariates and linear control over the rerandomized covariates. We introduce several new rerandomization schemes, allowing for imbalance metrics based on nonlinear estimators. We also propose a novel minimax scheme that uses pilot data or prior information to minimize the computational cost of rerandomization, subject to a strict bound on statistical efficiency. While the asymptotic distribution of generalized method of moments (GMM) estimators under stratified rerandomization is generically non-normal, we show how to restore asymptotic normality using ex-post linear adjustment tailored to the stratification. This enables simple asymptotically exact inference on superpopulation parameters, as well as efficient conservative inference on finite population parameters.

翻译：本文研究精细分层再随机化设计下的因果参数估计与推断。该设计首先利用基线协变量将单元匹配至不同组别（如配对组），随后在组内反复随机化处理分配直至满足平衡性准则。我们证明，精细分层再随机化本质上通过设计实现了部分线性回归调整，对分层协变量提供非参数控制，同时对再随机化协变量实现线性控制。我们提出了若干新型再随机化方案，支持基于非线性估计量的不平衡度量。此外，我们设计了一种新颖的极小极大化方案，该方案利用先导数据或先验信息，在严格限定统计效率损失的条件下最小化再随机化的计算成本。尽管分层再随机化下广义矩估计量（GMM）的渐近分布通常非正态，我们展示了如何通过针对分层结构定制的后验线性调整恢复渐近正态性。这为超总体参数提供了简便的渐近精确推断方法，并为有限总体参数实现了高效的保守推断。