# Beyond the Average: Distributional Causal Inference under Imperfect Compliance

arXiv: https://arxiv.org/abs/2509.15594 · HTML: https://mlsanity.com/paper/2509.15594/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 86 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 23 of 23)

- [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)
- [Robust and Agnostic Learning of Conditional Distributional Treatment Effects](https://mlsanity.com/paper/2205.11486/) (2022)
- [Distributional synthetic controls](https://mlsanity.com/paper/2001.06118/) (2020)
- [Decomposing Treatment Effect Variation](https://mlsanity.com/paper/1605.06566/) (2016)
- [Estimating Potential Outcome Distributions with Collaborating Causal Networks](https://mlsanity.com/paper/2110.01664/) (2021)
- [When is the estimated propensity score better? High-dimensional analysis and bias correction](https://mlsanity.com/paper/2303.17102/) (2023)
- [On Efficient Estimation of Distributional Treatment Effects under Covariate-Adaptive Randomization](https://mlsanity.com/paper/2506.05945/) (2025)
- [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)
- [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)
- [Instrumental Variable Estimation of Distributional Causal Effects](https://mlsanity.com/paper/2406.19986/) (2024)
- [A General Form of Covariate Adjustment in Randomized Clinical Trials](https://mlsanity.com/paper/2306.10213/) (2023)
- [Estimating Causal Effects of Discrete and Continuous Treatments with Binary Instruments](https://mlsanity.com/paper/2403.05850/) (2024)
- [Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance](https://mlsanity.com/paper/2201.13004/) (2022)
- [A decorrelation method for general regression adjustment in randomized experiments](https://mlsanity.com/paper/2311.10076/) (2023)
- [A unified framework for covariate adjustment under stratified randomization](https://mlsanity.com/paper/2312.01266/) (2023)
- [Efficient and Scalable Estimation of Distributional Treatment Effects with Multi-Task Neural Networks](https://mlsanity.com/paper/2507.07738/) (2025)

## Built on by (most cited first, 2 of 2)

- [Modeling Covariate Transition for Efficient Estimation of Longitudinal Treatment Effects in Randomized Experiments](https://mlsanity.com/paper/2605.31443/) (2026)
- [FinInvest-GTCN: Explainable Graph-Temporal-Causal Modeling for Risk-Aware Investment Decision Optimization](https://mlsanity.com/paper/2606.28933/) (2026)

## Abstract (arXiv)

We study the estimation of distributional treatment effects in randomized experiments with imperfect compliance. When participants do not adhere to their assigned treatments, we leverage treatment assignment as an instrumental variable to identify the local distributional treatment effect-the difference in outcome distributions between treatment and control groups for the subpopulation of compliers. We propose a regression-adjusted estimator based on a distribution regression framework with Neyman-orthogonal moment conditions, enabling robustness and flexibility with high-dimensional covariates. Our approach accommodates continuous, discrete, and mixed discrete-continuous outcomes, and applies under a broad class of covariate-adaptive randomization schemes, including stratified block designs and simple random sampling. We derive the estimator's asymptotic distribution and show that it achieves the semiparametric efficiency bound. Simulation results demonstrate favorable finite-sample performance, and we demonstrate the method's practical relevance in an application to the Oregon Health Insurance Experiment.