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.

翻译：尽管完全随机化被广泛视为因果推断的金标准，但在有限样本中协变量失衡仍可能偶然发生。重随机化已成为改善处理组间协变量平衡、提升因果效应估计精度的有效工具。现有研究主要关注平均处理效应，而分位数处理效应（QTEs）通过捕捉结果变量的分布变化，为处理异质性提供了更丰富的表征，这对政策评估和公平导向研究至关重要。本文在有限总体框架下建立了重随机化条件下QTE估计量的渐近性质，且未对协变量或结果变量施加任何分布或建模假设。该估计量呈现出非高斯渐近分布，表现为高斯随机变量与截断高斯随机变量的线性组合。为便于统计推断，我们提出了保守的方差估计量并构建了相应的置信区间。理论分析表明，在温和的正则条件下，重随机化相比完全随机化能提升估计效率。模拟研究进一步支持了理论发现，并阐明了重随机化在QTE估计中的实际优势。