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

arXiv: https://arxiv.org/abs/2506.05945 · HTML: https://mlsanity.com/paper/2506.05945/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 88 references that are in the map.
- First posted on arXiv 6 Jun 2025.

## Builds on (most cited first, 25 of 25)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [The Influence Function of Semiparametric Estimators](https://mlsanity.com/paper/1508.01378/) (2015)
- [Program Evaluation and Causal Inference with High-Dimensional Data](https://mlsanity.com/paper/1311.2645/) (2013)
- [Localized Debiased Machine Learning: Efficient Inference on Quantile Treatment Effects and Beyond](https://mlsanity.com/paper/1912.12945/) (2019)
- [Designing and Deploying Online Field Experiments](https://mlsanity.com/paper/1409.3174/) (2014)
- [Robust and Agnostic Learning of Conditional Distributional Treatment Effects](https://mlsanity.com/paper/2205.11486/) (2022)
- [Machine Learning for Variance Reduction in Online Experiments](https://mlsanity.com/paper/2106.07263/) (2021)
- [Causal isotonic calibration for heterogeneous treatment effects](https://mlsanity.com/paper/2302.14011/) (2023)
- [Estimating Potential Outcome Distributions with Collaborating Causal Networks](https://mlsanity.com/paper/2110.01664/) (2021)
- [Proximal Causal Learning of Conditional Average Treatment Effects](https://mlsanity.com/paper/2301.10913/) (2023)
- [Regression Adjustment for Estimating Distributional Treatment Effects in Randomized Controlled Trials](https://mlsanity.com/paper/2407.14074/) (2024)
- [Estimating Distributional Treatment Effects in Randomized Experiments: Machine Learning for Variance Reduction](https://mlsanity.com/paper/2407.16037/) (2024)
- [Causal-DRF: Conditional Kernel Treatment Effect Estimation using Distributional Random Forest](https://mlsanity.com/paper/2411.08778/) (2024)
- [Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes](https://mlsanity.com/paper/1608.05142/) (2016)
- [Quantile Treatment Effects in Difference in Differences Models under Dependence Restrictions and with only Two Time Periods](https://mlsanity.com/paper/1702.03618/) (2017)
- [Regression-Adjusted Estimation of Quantile Treatment Effects under Covariate-Adaptive Randomizations](https://mlsanity.com/paper/2105.14752/) (2021)
- [Covariate Adjustment in Stratified Experiments](https://mlsanity.com/paper/2302.03687/) (2023)
- [Inference under Covariate-Adaptive Randomization with Multiple Treatments](https://mlsanity.com/paper/1806.04206/) (2018)
- [A General Form of Covariate Adjustment in Randomized Clinical Trials](https://mlsanity.com/paper/2306.10213/) (2023)

## Built on by (most cited first, 6 of 6)

- [Beyond the Average: Distributional Causal Inference under Imperfect Compliance](https://mlsanity.com/paper/2509.15594/) (2025)
- [Efficient and Scalable Estimation of Distributional Treatment Effects with Multi-Task Neural Networks](https://mlsanity.com/paper/2507.07738/) (2025)
- [GDR-learners: Orthogonal Learning of Generative Models for Potential Outcomes](https://mlsanity.com/paper/2509.22953/) (2025)
- [Fast Rerandomization for Balancing Covariates in Randomized Experiments: A Metropolis-Hastings Framework](https://mlsanity.com/paper/2602.07613/) (2026)
- [Distributional Causal Mediation via Conditional Generative Modeling](https://mlsanity.com/paper/2605.01765/) (2026)
- [Modeling Covariate Transition for Efficient Estimation of Longitudinal Treatment Effects in Randomized Experiments](https://mlsanity.com/paper/2605.31443/) (2026)

## Abstract (arXiv)

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.