Rerandomization for quantile treatment effects

TL;DR

This paper investigates the use of rerandomization to improve the estimation of quantile treatment effects (QTEs), establishing their asymptotic properties and demonstrating efficiency gains over complete randomization through theoretical analysis and simulations.

Contribution

It provides the first asymptotic analysis of QTE estimators under rerandomization without distributional assumptions, introducing a new variance estimator and confidence intervals.

Findings

Rerandomization improves efficiency of QTE estimates.

The asymptotic distribution of the QTE estimator is non-Gaussian.

Simulation results confirm theoretical efficiency gains.

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.