Finely Stratified Rerandomization Designs

TL;DR

This paper investigates finely stratified rerandomization designs for causal inference, introducing new methods for balancing covariates, controlling estimation error, and ensuring valid inference in complex experimental setups.

Contribution

It introduces novel stratified rerandomization schemes, including nonlinear imbalance metrics and a minimax approach, with methods to restore asymptotic normality and derive variance bounds.

Findings

Rerandomization achieves partial linear adjustment by design.

New imbalance metrics based on nonlinear estimators improve covariate balance.

Variance bounds enable conservative and exact inference for causal parameters.

Abstract

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 forms of rerandomization, allowing for imbalance metrics based on nonlinear estimators, and proposing a minimax scheme that minimizes the computational cost of rerandomization subject to a bound on estimation error. While the asymptotic distribution of 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. We derive new variance bounds that enable conservative inference on finite population causal parameters, and provide asymptotically exact inference on their superpopulation counterparts.