{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T01:49:04Z","timestamp":1790300944008,"version":"4.1.0"},"reference-count":53,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T00:00:00Z","timestamp":1695686400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"name":"Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science"},{"DOI":"10.13039\/501100004106","name":"East China Normal University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004106","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ministry of Education of the People\u2019s Republic of China"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U23A2064"],"award-info":[{"award-number":["U23A2064"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,5,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>While model selection is a well-studied topic in parametric and nonparametric regression or density estimation, selection of possibly high-dimensional nuisance parameters in semiparametric problems is far less developed. In this paper, we propose a selective machine learning framework for making inferences about a finite-dimensional functional defined on a semiparametric model, when the latter admits a doubly robust estimating function and several candidate machine learning algorithms are available for estimating the nuisance parameters. We introduce a new selection criterion aimed at bias reduction in estimating the functional of interest based on a novel definition of pseudo risk inspired by the double robustness property. Intuitively, the proposed criterion selects a pair of learners with the smallest pseudo risk, so that the estimated functional is least sensitive to perturbations of a nuisance parameter. We establish an oracle property for a multi-fold cross-validation version of the new selection criterion that states that our empirical criterion performs nearly as well as an oracle with a priori knowledge of the pseudo risk for each pair of candidate learners. Finally, we apply the approach to model selection of a semiparametric estimator of average treatment effect given an ensemble of candidate machine learners to account for confounding in an observational study that we illustrate in simulations and a data application.<\/jats:p>","DOI":"10.1093\/biomet\/asad055","type":"journal-article","created":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T21:26:10Z","timestamp":1695849970000},"page":"517-535","source":"Crossref","is-referenced-by-count":6,"title":["Selective machine learning of doubly robust functionals"],"prefix":"10.1093","volume":"111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9957-7955","authenticated-orcid":false,"given":"Y","family":"Cui","sequence":"first","affiliation":[{"name":"School of Management & Center for Data Science, Zhejiang University , 866 Yuhangtang Road , Hangzhou, Zhejiang 310058, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E J","family":"Tchetgen Tchetgen","sequence":"additional","affiliation":[{"name":"Department of Statistics and Data Science, The Wharton School, University of Pennsylvania , 265 South 37th Street , Philadelphia, Pennsylvania 19104, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,9,26]]},"reference":[{"key":"2024051307572084500_asad055-B1","author":"Austern","year":"2020"},{"key":"2024051307572084500_asad055-B2","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1111\/j.1541-0420.2005.00377.x","article-title":"Doubly robust estimation in missing data and causal inference models","volume":"61","author":"Bang","year":"2005","journal-title":"Biometrics"},{"key":"2024051307572084500_asad055-B3","first-page":"484","article-title":"A nonparametric super-efficient estimator of the average treatment effect","volume":"35","author":"Benkeser","year":"2020","journal-title":"Statist. 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