Conditional Distributional Treatment Effects: Doubly Robust Estimation and Testing
2026-03-17 • Machine Learning
Machine Learning
AI summaryⓘ
The authors propose a new way to measure how treatments affect not just the average outcome but the whole distribution of outcomes, including things like variability or risk for different groups. They develop a reliable method to estimate this effect, which performs optimally in certain technical senses. Using this, the authors create a test to check if the distributions of potential outcomes are the same across groups, which works under broader conditions than previous tests and has strong guarantees for accuracy. They also provide exact formulas for measuring differences and an efficient algorithm to run their test without heavy computation.
conditional treatment effectsoutcome distributiondoubly robust estimatorminimax optimalitymaximum mean discrepancy (MMD)type 1 errorpermutation testcovariate-dependent effects
Authors
Saksham Jain, Alex Luedtke
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. 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.