Primary Submission Category: Design of Experiments
Sequential Rerandomization Under Ellipsoidal and Rectangular Constraints
Authors: Kyle Schindl, Zach Branson,
Presenting Author: Kyle Schindl*
When designing a randomized experiment, one way to ensure treatment and control groups exhibit similar covariate distributions is to randomize treatment until some prespecified level of covariate balance is satisfied; this strategy is known as rerandomization. Most rerandomization methods utilize balance metrics based on ellipsoidal or rectangular constraints on the covariate mean-differences. In this work, we derive general results for treatment-versus-control rerandomization schemes that employ either type of constraint for covariate balance. In addition to allowing researchers to quickly derive properties of rerandomization schemes not previously considered, our theoretical results provide guidance on how to choose the constraint in practice. After deriving optimal choices of constraints for covariate balance and variance reduction, we extend this framework to sequential experiments. There, we develop an optimal updating strategy such that experimenters can change their rerandomization strategy after observing the covariates (or outcomes) from previous groups. This leads to substantial efficiency gains over traditional sequential experimental design strategies.