Gaussian and bootstrap approximation for matching-based average treatment effect estimators
Abstract
We establish Gaussian approximation bounds for covariate and rank-matching-based Average Treatment Effect (ATE) estimators. By analyzing these estimators through the lens of stabilization theory, we employ the Malliavin–Stein method to derive our results. Our bounds precisely quantify the impact of key problem parameters, including the number of matches and treatment balance, on the accuracy of the Gaussian approximation. Additionally, we develop multiplier bootstrap procedures to estimate the limiting distribution in a fully data-driven manner, and we leverage the derived Gaussian approximation results to further obtain bootstrap approximation bounds. Our work not only introduces a novel theoretical framework for commonly used ATE estimators, but also provides data-driven methods for constructing nonasymptotically valid confidence intervals.
Fields of Study & Subjects
Statistical Methods and Inference
Publication details
- Journal / source
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Volume
- 54
- Issue
- 4
- Pages
- 2164–2190
- Publication date
- 1 August 2026
- Language
- EN