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Rerandomization for quantile treatment effects

Tingxuan Han, Yuhao Wang

TL;DR

This paper develops a finite-population theory for quantile treatment effects under rerandomization, showing that the QTE estimator has a non Gaussian, mixture type asymptotic distribution when covariate balance is improved via ReM. It introduces estimable upper bounds and a conservative variance estimator to enable valid inference, and proves that ReM reduces asymptotic variance relative to complete randomization under mild conditions. The authors provide a detailed inference framework including confidence intervals and demonstrate, through extensive simulations and a real data example, that ReM yields efficiency gains and robust coverage for QTE estimation in both linear and nonlinear settings. The work extends design based causal inference to distributional treatment effects, offering practical tools for policy evaluation and equity-focused research while highlighting directions for regression adjusted QTE under ReM.

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.

Rerandomization for quantile treatment effects

TL;DR

This paper develops a finite-population theory for quantile treatment effects under rerandomization, showing that the QTE estimator has a non Gaussian, mixture type asymptotic distribution when covariate balance is improved via ReM. It introduces estimable upper bounds and a conservative variance estimator to enable valid inference, and proves that ReM reduces asymptotic variance relative to complete randomization under mild conditions. The authors provide a detailed inference framework including confidence intervals and demonstrate, through extensive simulations and a real data example, that ReM yields efficiency gains and robust coverage for QTE estimation in both linear and nonlinear settings. The work extends design based causal inference to distributional treatment effects, offering practical tools for policy evaluation and equity-focused research while highlighting directions for regression adjusted QTE under ReM.

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.
Paper Structure (19 sections, 10 theorems, 232 equations)

This paper contains 19 sections, 10 theorems, 232 equations.

Table of Contents

  1. Introduction
  2. Problem set up
  3. Finite population and QTE estimation
  4. Completely randomized experiments and rerandomization
  5. Non-asymptotic convergence of empirical cumulant estimators
  6. Asymptotic convergence of QTE estimators
  7. Large-sample inference under ReM
  8. Simulation analysis
  9. Numerical simulations
  10. Real-data-based simulations
  11. Summary and Discussion
  12. Disclosure statement
  13. Data Availability Statement
  14. Proof
  15. Proof of Theorem \ref{['thm:qz']}
  16. ...and 4 more sections

Key Result

Lemma 1

Under a completely randomized experiment, if $\boldsymbol{V}$ is nonsingular, then the Kolmogorov distance $\Delta_n$ defined in eq:delta_n converges to zero if $\gamma_n \to 0$ as $n \to \infty$.

Theorems & Definitions (18)

  • Lemma 1
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Corollary 1
  • Remark 1
  • Proposition 1
  • Theorem 6
  • ...and 8 more