{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T06:07:24Z","timestamp":1791439644334,"version":"4.3.3"},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2020,6,14]],"date-time":"2020-06-14T00:00:00Z","timestamp":1592092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"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":[[2020,12,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The infinite-dimensional information operator for the nuisance parameter plays a key role in semiparametric inference, as it is closely related to the regular estimability of the target parameter. Calculation of information operators has traditionally proceeded in a case-by-case manner and has often entailed lengthy derivations with complicated arguments. We develop a unified framework for this task by exploiting commonality in the form of semiparametric likelihoods. The general formula developed allows one to derive information operators with simple calculus and, if necessary at all, a minimal amount of probabilistic evaluation. This streamlined approach shows its simplicity and versatility in application to a number of existing models as well as a new model of practical interest.<\/jats:p>","DOI":"10.1093\/biomet\/asaa037","type":"journal-article","created":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T19:09:59Z","timestamp":1587668999000},"page":"983-995","source":"Crossref","is-referenced-by-count":1,"title":["A unified approach to the calculation of information operators in semiparametric models"],"prefix":"10.1093","volume":"107","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8626-9822","authenticated-orcid":false,"given":"Lu","family":"Mao","sequence":"first","affiliation":[{"name":"Department of Biostatistics and Medical Informatics, School of Medicine and Public Health, University of Wisconsin-Madison, Madison, Wisconsin 53726, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,6,14]]},"reference":[{"key":"2020121116434131300_B1","volume-title":"Efficient and Adaptive Estimation for Semiparametric Models","author":"Bickel,","year":"1993"},{"key":"2020121116434131300_B2","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1093\/biomet\/66.3.429","article-title":"Linear regression with censored data","volume":"66","author":"Buckley,","year":"1979","journal-title":"Biometrika"},{"key":"2020121116434131300_B3","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1093\/biomet\/62.2.269","article-title":"Partial likelihood","volume":"62","author":"Cox,","year":"1975","journal-title":"Biometrika"},{"key":"2020121116434131300_B4","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1214\/lnms\/1215452217","volume-title":"Analysis of Censored Data","author":"Huang,","year":"1995"},{"key":"2020121116434131300_B5","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1214\/aos\/1032894452","article-title":"Efficient estimation for the proportional hazards model with interval censoring","volume":"24","author":"Huang,","year":"1996","journal-title":"Ann. 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