A0663
Title: Causal inference with flexible covariate adjustment under rerandomization
Authors: Bingkai Wang - University of Michigan (United States) [presenting]
Abstract: Rerandomization is an effective treatment allocation procedure in randomized experiments. For estimating the average treatment effect, rerandomization has been previously shown to improve the precision of the unadjusted and the linearly-adjusted estimators over simple randomization without compromising consistency. However, it remains unclear whether such results apply more generally to the class of M-estimators, including the g-computation formula with generalized linear regression and doubly robust methods, and more broadly, to efficient estimators with data-adaptive machine learners. Using a super-population framework, the asymptotic theory is developed for a more general class of covariate-adjusted estimators under rerandomization and its stratified extension. It is proven that the asymptotic linearity and the influence function remain identical for any M-estimator under simple randomization and rerandomization, but rerandomization may lead to a non-Gaussian asymptotic distribution. It is further explained, drawing examples from several common M-estimators, that asymptotic normality can be achieved if rerandomization variables are appropriately adjusted for in the final estimator. These results are extended to stratified rerandomization. Finally, the asymptotic theory is studied for efficient estimators based on data-adaptive machine learners, and their efficiency optimality is proven under rerandomization and stratified rerandomization.
