On Optimal Rerandomization Designs

Abstract Blocking is commonly used in randomized experiments to increase efficiency of estimation. A generalization blocking removes allocations with imbalance covariate distributions between treated and control units, then randomizes within the remaining set balance. This idea rerandomization was formalized by Morgan Rubin (Annals Statistics, 2012, 40, 1263–1282), who suggested using Mahalanobis distance means as criterion for removing unbalanced allocations. Kallus (Journal Royal Statistical Society, Series B: Methodology, 2018, 80, 85–112) proposed reducing balanced minimum. Here we discuss implication such an ‘optimal’ design inferences units sample population from which were randomly drawn. We argue that, general, it a bad seek optimal inference because that typically only reflects uncertainty random sampling usually hypothetical, not randomization treatment versus control.