Conditional Distributional Treatment Effects: Doubly Robust Estimation and Testing
This addresses the need to understand treatment effects beyond averages in fields like medicine and economics, representing a novel methodological advance rather than an incremental improvement.
The authors tackled the problem of estimating how treatments affect entire outcome distributions rather than just averages, proposing a novel estimand for conditional distributional treatment effects and developing a doubly robust estimator that is minimax optimal. They also created a test for global homogeneity of conditional potential outcome distributions with provable type 1 error control and consistency, providing exact closed-form expressions and a computationally efficient algorithm.
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.