Gaussian and Bootstrap Approximation for Matching-based Average Treatment Effect Estimators

TL;DR

This paper develops Gaussian approximation bounds and bootstrap methods for matching-based ATE estimators, providing theoretical insights and practical tools for accurate inference in causal studies.

Contribution

It introduces a novel theoretical framework using stabilization theory and Malliavin-Stein method, along with data-driven bootstrap procedures for ATE estimators.

Findings

Gaussian approximation bounds depend on number of matches and treatment balance

Multiplier bootstrap procedures accurately estimate the limiting distribution

Provides non-asymptotic confidence intervals for ATE estimates

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 non-asymptotically valid confidence intervals.