Finely Stratified Rerandomization Designs

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.