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To improve efficiency, multiple instruments are routinely used, raising concerns about bias due to possible violation of the instrumental variable assumptions. To address such concerns, we introduce a new class of G-estimators that are guaranteed to remain consistent and asymptotically normal for the causal effect of interest provided that a set of at least $\\gamma$ out of $K$ candidate instruments are valid, for $\\gamma \\leqslant K$ set by the analyst ex ante without necessarily knowing the identities of the valid and invalid instruments. We provide formal semiparametric efficiency theory supporting our results. Simulation studies and applications to UK Biobank data demonstrate the superior empirical performance of the proposed estimators compared with competing methods.<\/jats:p>","DOI":"10.1093\/biomet\/asad011","type":"journal-article","created":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T12:39:02Z","timestamp":1676464742000},"page":"953-971","source":"Crossref","is-referenced-by-count":12,"title":["Semiparametric efficient G-estimation with invalid instrumental variables"],"prefix":"10.1093","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0122-9993","authenticated-orcid":false,"given":"B","family":"Sun","sequence":"first","affiliation":[{"name":"National University of Singapore Department of Statistics and Data Science, , 6 Science Drive 2, 117546 Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3048-9823","authenticated-orcid":false,"given":"Z","family":"Liu","sequence":"additional","affiliation":[{"name":"Columbia University Department of Biostatistics, , 722 West 168th St., New York, New York 10032, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E J","family":"Tchetgen Tchetgen","sequence":"additional","affiliation":[{"name":"The Wharton School, University of Pennsylvania Department of Statistics and Data Science, , 265 South 37th Street, Philadelphia, Pennsylvania 19104, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,2,15]]},"reference":[{"key":"2023111615232994200_B1","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/S0304-4076(02)00201-4","article-title":"Semiparametric instrumental variable estimation of treatment response models","volume":"113","author":"Abadie,","year":"2003","journal-title":"J. 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