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 covariates used for stratification, and linear control over the rerandomization covariates. We also introduce novel rerandomization criteria, allowing for nonlinear imbalance metrics and proposing a minimax scheme that optimizes the balance criterion using pilot data or prior information provided by the researcher. While the asymptotic distribution of generalized method of moments (GMM) estimators under stratified rerandomization is generically non-Gaussian, we show how to restore asymptotic normality using optimal ex-post linear adjustment. This allows us to provide simple asymptotically exact inference methods for superpopulation parameters, as well as efficient conservative inference methods for 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，该设计利用基线协变量将单元匹配至各组（如匹配对），然后在组内重复随机化处理分配直至满足平衡准则。我们证明精细分层再随机化通过设计实现了部分线性回归调整，对用于分层的协变量提供非参数控制，并对再随机化协变量提供线性控制。我们还提出了新颖的再随机化准则，允许使用非线性不平衡度量，并提出一种极小极大方案，该方案利用试验数据或研究者提供的先验信息优化平衡准则。虽然广义矩估计（GMM）在分层再随机化下的渐近分布通常为非高斯分布，但我们展示了如何通过最优事后线性调整恢复渐近正态性。这使得我们能够为超总体参数提供简单的渐近精确推断方法，并为有限总体参数提供高效的保守推断方法。