Zhaoyang Shi, Chinmoy Bhattacharjee, Krishnakumar Balasubramanian, Wolfgang Polonik
arXiv 22 Dec 2024 · Mathematics — Statistics Theory
arXiv:2412.17181 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | A. Abadie and G. W. Imbens (2006) Large sample properties of matching estimators for average treatment effects | 1.000 | 7 | 3 | 100% |
| 2 | A. Abadie and G. W. Imbens (2011) Bias-corrected matching estimators for average treatment effects | 1.000 | 5 | 3 | 100% |
| 3 | P. R. Rosenbaum (2010) Design of observational studies, volume 10 | 1.000 | 5 | 3 | 100% |
| 4 | Z. Lin, P. Ding, and F. Han (2023) Estimation based on nearest neighbor matching: From density ratio to average treatment effect | 0.741 | 27 | 6 | 41% |
| 5 | A. Abadie and G. W. Imbens (2008) On the failure of the bootstrap for matching estimators | 0.737 | 3 | 2 | 100% |
| 6 | R. Lachièze-Rey, M. Schulte, and J. E. Yukich (2019) Normal approximation for stabilizing functionals | 0.705 | 20 | 4 | 35% |
| 7 | P. R. Rosenbaum (2005) An exact distribution-free test comparing two multivariate distributions based on adjacency | 0.644 | 2 | 2 | 100% |
| 8 | Z. Shi, K. Balasubramanian, and W. Polonik (2024) A flexible approach for normal approximation of geometric and topological statistics | 0.644 | 2 | 2 | 100% |
| 9 | Z. Shi, C. Bhattacharjee, K. Balasubramanian, and W. Polonik (2024) Multivariate Gaussian Approximation for Random Forest via Region-based Stabilization | 0.644 | 2 | 2 | 100% |
| 10 | M. D. Cattaneo, F. Han, and Z. Lin (2023) On Rosenbaum's rank-based matching estimator | 0.638 | 27 | 6 | 26% |
Showing the top 10 of 33 scored citations.