# Conditional Distributional Treatment Effects: Doubly Robust Estimation and Testing

arXiv: https://arxiv.org/abs/2603.16829 · HTML: https://mlsanity.com/paper/2603.16829/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 55 references that are in the map.
- First posted on arXiv 17 Mar 2026.

## Builds on (most cited first, 17 of 17)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [Counterfactual Mean Embeddings](https://mlsanity.com/paper/1805.08845/) (2018)
- [A Witness Two-Sample Test](https://mlsanity.com/paper/2102.05573/) (2021)
- [On the Optimality of Kernel-Embedding Based Goodness-of-Fit Tests](https://mlsanity.com/paper/1709.08148/) (2017)
- [Robust and Agnostic Learning of Conditional Distributional Treatment Effects](https://mlsanity.com/paper/2205.11486/) (2022)
- [Dimension-agnostic inference using cross U-statistics](https://mlsanity.com/paper/2011.05068/) (2020)
- [One-Step Estimation of Differentiable Hilbert-Valued Parameters](https://mlsanity.com/paper/2303.16711/) (2023)
- [An Efficient Doubly-Robust Test for the Kernel Treatment Effect](https://mlsanity.com/paper/2304.13237/) (2023)
- [Neural-Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2403.10859/) (2024)
- [Confidence and Uncertainty Assessment for Distributional Random Forests](https://mlsanity.com/paper/2302.05761/) (2023)
- [Causal-DRF: Conditional Kernel Treatment Effect Estimation using Distributional Random Forest](https://mlsanity.com/paper/2411.08778/) (2024)
- [Network and Panel Quantile Effects Via Distribution Regression](https://mlsanity.com/paper/1803.08154/) (2018)
- [Minimax Optimal Kernel Two-Sample Tests with Random Features](https://mlsanity.com/paper/2502.20755/) (2025)

## Built on by (most cited first, 3 of 3)

- [Measuring Differences between Conditional Distributions using Kernel Embeddings](https://mlsanity.com/paper/2605.02260/) (2026)
- [Extended Wasserstein-GAN Approach to Causal Distribution Learning: Density-Free Estimation and Minimax Optimality](https://mlsanity.com/paper/2605.10206/) (2026)
- [Wasserstein Causal Forests for Distribution-Valued Outcomes](https://mlsanity.com/paper/2609.35898/) (2026)

## Abstract (arXiv)

Beyond conditional average treatment effects, treatments may impact the entire outcome distribution in covariate-dependent ways, for example, by altering the variance or tail risks for specific subpopulations. We propose a novel estimand to capture such conditional distributional treatment effects, and develop a doubly robust estimator that is minimax optimal in the local asymptotic sense. Using this, we develop a test for the global homogeneity of conditional potential outcome distributions that accommodates discrepancies beyond the maximum mean discrepancy (MMD), has provably valid type 1 error, and is consistent against fixed alternatives---the first test, to our knowledge, with such guarantees in this setting. We then provide a test that aggregates evidence across a grid of kernel-bandwidth choices. Furthermore, we derive exact closed-form expressions for two natural discrepancies (including the MMD), and provide a computationally efficient, permutation-free algorithm for our test.