Rerandomization for quantile treatment effects

Abstract: Although complete randomization is widely regarded as the gold standard for causal inference, covariate imbalance can still arise by chance in finite samples. Rerandomization has emerged as an effective tool to improve covariate balance across treatment groups and enhance the precision of causal effect estimation. While existing work focuses on average treatment effects, quantile treatment effects (QTEs) provide a richer characterization of treatment heterogeneity by capturing distributional shifts in outcomes, which is crucial for policy evaluation and equity-oriented research. In this article, we establish the asymptotic properties of the QTE estimator under rerandomization within a finite-population framework, without imposing any distributional or modeling assumptions on the covariates or outcomes.The estimator exhibits a non-Gaussian asymptotic distribution, represented as a linear combination of Gaussian and truncated Gaussian random variables. To facilitate inference, we propose a conservative variance estimator and construct corresponding confidence interval. Our theoretical analysis demonstrates that rerandomization improves efficiency over complete randomization under mild regularity conditions. Simulation studies further support the theoretical findings and illustrate the practical advantages of rerandomization for QTE estimation.