Variance reduction through rerandomization and covariate adjustment in factorial design using simulation

Abstract

This paper develops a unified framework for improving statistical efficiency in factorial experiments by integrating rerandomization and regression-based covariate adjustment. We derive new theoretical results showing that the efficiency gains from these approaches are complementary and multiplicative, driven by the acceptance probability and the predictive power of covariates. We further characterize the covariance structure of factorial effect estimators under constrained randomization and provide comprehensive simulation evidence demonstrating substantial improvements in precision. The results offer new insights into combining design-based and model-assisted strategies for multi-factor experimental settings.