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

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Summary

The paper discusses the Gaussian approximation bounds for matching-based and rank-based average treatment effect (ATE) estimators. The authors provide non-asymptotic bounds for the Kolmogorov distance between the estimators and a normal distribution, allowing for a more accurate assessment of the estimators' performance.

Highlights

• The paper provides non-asymptotic Gaussian approximation bounds for matching-based and rank-based ATE estimators.
• The bounds are derived using the Malliavin-Stein method and stabilization theory.
• The authors consider both covariate-based and rank-based matching, including the CDF-rank-based estimator.
• The bounds depend on key parameters such as the number of matches, treatment balance, and the convergence rate of the sample variance.
• The paper also discusses the application of the Gaussian approximation results to construct non-asymptotically valid confidence intervals.
• The authors provide a multiplier bootstrap procedure to estimate the limiting distribution and establish bootstrap approximation rates.
• The paper compares the rates of convergence for covariate-based and CDF-rank-based ATE estimators in the univariate setting.

Key Insights

• The Gaussian approximation bounds provide a more accurate assessment of the performance of matching-based and rank-based ATE estimators, especially in small samples.
• The bounds highlight the importance of considering the number of matches, treatment balance, and the convergence rate of the sample variance when evaluating the performance of ATE estimators.
• The use of stabilization theory and the Malliavin-Stein method allows for the derivation of non-asymptotic bounds, which are more informative than asymptotic results.
• The CDF-rank-based estimator is shown to have a slower rate of convergence compared to the covariate-based estimator in the univariate setting, highlighting the importance of choosing the correct estimator for a given problem.
• The multiplier bootstrap procedure provides a practical method for estimating the limiting distribution and constructing non-asymptotically valid confidence intervals.
• The results of the paper have implications for the design of experiments and the choice of estimators in practice, highlighting the need for careful consideration of the parameters involved.
• The paper contributes to the growing literature on non-asymptotic inference and provides new insights into the performance of matching-based and rank-based ATE estimators.

Mindmap

Citation

Shi, Z., Bhattacharjee, C., Balasubramanian, K., & Polonik, W. (2024). Gaussian and Bootstrap Approximation for Matching-based Average Treatment Effect Estimators (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.17181