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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 nonasymptotically valid confidence intervals.<\/jats:p>","DOI":"10.1214\/26-aos2647","type":"journal-article","created":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T08:21:41Z","timestamp":1787041301000},"page":"2164-2190","source":"Crossref","is-referenced-by-count":0,"title":["Gaussian and bootstrap approximation for matching-based average treatment effect estimators"],"prefix":"10.1214","volume":"54","author":[{"given":"Zhaoyang","family":"Shi","sequence":"first","affiliation":[{"name":"Department of Statistics, Harvard University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chinmoy","family":"Bhattacharjee","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Universit\u00e4t Hamburg"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Krishnakumar","family":"Balasubramanian","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California, Davis"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wolfgang","family":"Polonik","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California, Davis"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"108","reference":[{"key":"13","doi-asserted-by":"publisher","unstructured":"Lachi\u00e8ze-Rey, R.<\/small>, Schulte, M.<\/small> and Yukich, J. 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