On Efficient Estimation of Distributional Treatment Effects under Covariate-Adaptive Randomization

2025-06-06

AI Summary

This paper addresses the efficient estimation of distributional treatment effects (DTE) in covariate-adaptive randomization (CAR) experiments. We first derive the semiparametric efficient information bound for DTE under CAR and propose a regression-adjusted estimator that achieves this bound. Methodologically, we develop a flexible estimation framework grounded in distributional regression, enabling seamless integration of off-the-shelf machine learning models—such as random forests and neural networks—for high-dimensional covariate adjustment. We further establish rigorous asymptotic distribution theory and valid inference procedures. Simulation studies and an empirical application to microcredit data demonstrate that our estimator substantially improves estimation accuracy and statistical power relative to unadjusted and simple stratified estimators. To our knowledge, this is the first method that attains the semiparametric efficiency bound, scales to high dimensions, and is practically implementable for causal distributional inference under CAR designs.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper focuses on the estimation of distributional treatment effects in randomized experiments that use covariate-adaptive randomization (CAR). These include designs such as Efron's biased-coin design and stratified block randomization, where participants are first grouped into strata based on baseline covariates and assigned treatments within each stratum to ensure balance across groups. In practice, datasets often contain additional covariates beyond the strata indicators. We propose a flexible distribution regression framework that leverages off-the-shelf machine learning methods to incorporate these additional covariates, enhancing the precision of distributional treatment effect estimates. We establish the asymptotic distribution of the proposed estimator and introduce a valid inference procedure. Furthermore, we derive the semiparametric efficiency bound for distributional treatment effects under CAR and demonstrate that our regression-adjusted estimator attains this bound. Simulation studies and empirical analyses of microcredit programs highlight the practical advantages of our method.

Problem

• Estimating distributional treatment effects under covariate-adaptive randomization
• Incorporating additional covariates to improve estimation precision
• Achieving semiparametric efficiency bound for treatment effect estimates

Innovation

• Flexible distribution regression framework
• Leverages machine learning methods
• Attains semiparametric efficiency bound