{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T21:46:16Z","timestamp":1790631976506,"version":"4.1.0"},"reference-count":20,"publisher":"Oxford University Press (OUP)","issue":"4","funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,12,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Doubly robust estimators are widely used to draw inference about the average effect of a treatment. Such estimators are consistent for the effect of interest if either one of two nuisance parameters is consistently estimated. However, if flexible, data-adaptive estimators of these nuisance parameters are used, double robustness does not readily extend to inference. We present a general theoretical study of the behaviour of doubly robust estimators of an average treatment effect when one of the nuisance parameters is inconsistently estimated. We contrast different methods for constructing such estimators and investigate the extent to which they may be modified to also allow doubly robust inference. We find that while targeted minimum loss-based estimation can be used to solve this problem very naturally, common alternative frameworks appear to be inappropriate for this purpose. We provide a theoretical study and a numerical evaluation of the alternatives considered. Our simulations highlight the need for and usefulness of these approaches in practice, while our theoretical developments have broad implications for the construction of estimators that permit doubly robust inference in other problems.<\/jats:p>","DOI":"10.1093\/biomet\/asx053","type":"journal-article","created":{"date-parts":[[2017,9,11]],"date-time":"2017-09-11T15:13:15Z","timestamp":1505142795000},"page":"863-880","source":"Crossref","is-referenced-by-count":104,"title":["Doubly robust nonparametric inference on the average treatment\n          effect"],"prefix":"10.1093","volume":"104","author":[{"given":"D","family":"Benkeser","sequence":"first","affiliation":[{"name":"Department of Biostatistics and Bioinformatics, Emory University, 1518 Clifton Rd NE, Atlanta, Georgia 30322, U.S.A. benkeser@emory.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M","family":"Carone","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, University of Washington, 1705 NE Pacific Street, Box 357232, Seattle, Washington 98195, U.S.A. mcarone@uw.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M J Van Der","family":"Laan","sequence":"additional","affiliation":[{"name":"Division of Biostatistics, University of California, 108 Haviland Hall, Berkeley, California 94720, U.S.A. laan@berkeley.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P B","family":"Gilbert","sequence":"additional","affiliation":[{"name":"Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue North, PO Box 19024, Seattle, Washington 98109, U.S.A. pgilbert@scharp.org"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,10,16]]},"reference":[{"key":"2019071815503643300_B1","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1111\/j.1541-0420.2005.00377.x","article-title":"Doubly\n            robust estimation in missing data and causal inference\n            models.","volume":"61","author":"Bang","year":"2005","journal-title":"Biometrics"},{"key":"2019071815503643300_B2","author":"Benkeser","year":"2017","journal-title":"drtmle: Doubly-Robust Nonparametric\n            Estimation and Inference"},{"key":"2019071815503643300_B3","volume-title":"Efficient and Adaptive Estimation for Semiparametric\n            Models.","author":"Bickel","year":"1997"},{"key":"2019071815503643300_B4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-0027-2","volume-title":"Statistical\n            Estimation: Asymptotic Theory","author":"Ibragimov","year":"1981"},{"key":"2019071815503643300_B5","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1214\/07-STS227","article-title":"Demystifying double robustness: A comparison of alternative strategies\n            for estimating a population mean from incomplete data.","volume":"22","author":"Kang","year":"2007","journal-title":"Statist.\n            Sci."},{"key":"2019071815503643300_B6","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5769-1","volume-title":"Contributions to a General Asymptotic\n            Statistical Theory","author":"Pfanzagl","year":"1982"},{"key":"2019071815503643300_B7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2202\/1557-4679.1308","article-title":"The\n            relative performance of targeted maximum likelihood\n            estimators.","volume":"7","author":"Porter","year":"2011","journal-title":"Int. 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