Conditional Distributional Treatment Effects: Doubly Robust Estimation and Testing

Abstract: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.

Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST); Methodology (stat.ME)

arXiv:2603.16829 [stat.ML]

(or arXiv:2603.16829v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2603.16829 Focus to learn more arXiv-issued DOI via DataCite

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