{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T03:08:30Z","timestamp":1774840110482,"version":"3.50.1"},"reference-count":46,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T00:00:00Z","timestamp":1718323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper re-examines the work of Abadie &amp; Imbens (2016) on propensity score matching for average treatment effect estimation. We explore the asymptotic behaviour of these estimators when the number of nearest neighbours, M, grows with the sample size. It is shown, while not surprising, but technically nontrivial, that the modified estimators can improve upon the original fixed M-estimators in terms of efficiency. Additionally, we demonstrate the potential to attain the semiparametric efficiency lower bound when the propensity score admits some special structures, echoing the insight of Hahn (1998).<\/jats:p>","DOI":"10.1093\/biomet\/asae026","type":"journal-article","created":{"date-parts":[[2024,6,15]],"date-time":"2024-06-15T02:04:24Z","timestamp":1718417064000},"page":"1421-1428","source":"Crossref","is-referenced-by-count":1,"title":["On propensity score matching with a diverging number of matches"],"prefix":"10.1093","volume":"111","author":[{"given":"Yihui","family":"He","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Peking University , Beijing, BJ 100080,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fang","family":"Han","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Washington , B-317 Padelford Hall, Seattle, Washington 98195,","place":["U.S.A"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,6,14]]},"reference":[{"key":"2024112207520345800_asae026-B1","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1111\/j.1468-0262.2006.00655.x","article-title":"Large sample properties of matching estimators for average treatment effects","volume":"74","author":"Abadie","year":"2006","journal-title":"Econometrica"},{"key":"2024112207520345800_asae026-B2","doi-asserted-by":"crossref","first-page":"1537","DOI":"10.3982\/ECTA6474","article-title":"On the failure of the bootstrap for matching estimators","volume":"76","author":"Abadie","year":"2008","journal-title":"Econometrica"},{"key":"2024112207520345800_asae026-B3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1198\/jbes.2009.07333","article-title":"Bias-corrected matching estimators for average treatment effects","volume":"29","author":"Abadie","year":"2011","journal-title":"J. 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