Extend stabilization-based Gaussian approximation to the K-fold doubly robust matching ATE estimator

Develop Gaussian approximation bounds, using stabilization theory and the Malliavin–Stein method, for the K-fold partition-based doubly robust nearest-neighbor matching Average Treatment Effect (ATE) estimator of Lin et al. (2023). Specifically, construct non-asymptotic Kolmogorov distance bounds analogous to those proved for the single-sample bias-corrected matching estimator, quantifying the dependence on key parameters such as the number of matches M and treatment balance η, and establish how cross-fitting affects the radius of stabilization and the resulting rates.

Background

The paper develops non-asymptotic Gaussian approximation bounds for bias-corrected nearest-neighbor matching ATE estimators by combining stabilization theory with the Malliavin–Stein method. The derived bounds highlight how parameters like the number of matches and treatment balance affect approximation accuracy.

The authors note that Lin et al. (2023) analyze a cross-fitted (K-fold partition) doubly robust matching estimator. While the present paper’s stabilization-based analysis targets the single-sample estimator, the authors suggest that similar ideas could apply to the K-fold estimator but do not carry out the details. Extending the stabilization framework to cross-fitting would require analyzing how partitioning and averaging interact with local dependence and the radius of stabilization, and how these modifications influence non-asymptotic rates.