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

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  • Zhaoyang Shi
  • Chinmoy Bhattacharjee
  • Krishnakumar Balasubramanian
  • Wolfgang Polonik

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.

Suggested Citation

  • Zhaoyang Shi & Chinmoy Bhattacharjee & Krishnakumar Balasubramanian & Wolfgang Polonik, 2024. "Gaussian and Bootstrap Approximation for Matching-based Average Treatment Effect Estimators," Papers 2412.17181, arXiv.org.
    • Handle: RePEc:arx:papers:2412.17181
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    References listed on IDEAS

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    1. Paul R. Rosenbaum, 2005. "An exact distribution‐free test comparing two multivariate distributions based on adjacency," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 515-530, September.
    2. Alberto Abadie & Jann Spiess, 2022. "Robust Post-Matching Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 983-995, April.
    3. Rosenbaum, Paul R., 2010. "Design Sensitivity and Efficiency in Observational Studies," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 692-702.
    4. Alberto Abadie & Guido W. Imbens, 2008. "On the Failure of the Bootstrap for Matching Estimators," Econometrica, Econometric Society, vol. 76(6), pages 1537-1557, November.
    5. Alberto Abadie & Guido W. Imbens, 2006. "Large Sample Properties of Matching Estimators for Average Treatment Effects," Econometrica, Econometric Society, vol. 74(1), pages 235-267, January.
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