{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T07:28:41Z","timestamp":1791530921326,"version":"4.3.4"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2007,5,22]],"date-time":"2007-05-22T00:00:00Z","timestamp":1179792000000},"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\/100000054","name":"National Cancer Institute","doi-asserted-by":"publisher","award":["CA74552"],"award-info":[{"award-number":["CA74552"]}],"id":[{"id":"10.13039\/100000054","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007,6,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We consider functional measurement error models where the measurement error distribution is estimated non-parametrically. We derive a locally efficient semiparametric estimator but propose not to implement it owing to its numerical complexity. Instead, a plug-in estimator is proposed, where the measurement error distribution is estimated through non-parametric kernel methods based on multiple measurements. The root n consistency and asymptotic normality of the plug-in estimator are derived. Despite the theoretical inefficiency of the plug-in estimator, simulations demonstrate its near optimal performance. Computational advantages relative to the theoretically efficient estimator make the plug-in estimator practically appealing. Application of the estimator is illustrated by using the Framingham data example.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2007.00596.x","type":"journal-article","created":{"date-parts":[[2007,5,23]],"date-time":"2007-05-23T14:25:51Z","timestamp":1179930351000},"page":"429-446","source":"Crossref","is-referenced-by-count":18,"title":["Semiparametric estimators of functional measurement error models with unknown error"],"prefix":"10.1093","volume":"69","author":[{"given":"Peter","family":"Hall","sequence":"first","affiliation":[{"name":"Australian National University , Canberra , Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanyuan","family":"Ma","sequence":"additional","affiliation":[{"name":"Texas A&M University , College Station , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2007,5,22]]},"reference":[{"key":"2023040705374011100_","volume-title":"Efficient and Adaptive Estimation for Semiparametric Models","author":"Bickel","year":"1993"},{"key":"2023040705374011100_","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1214\/aos\/1176350358","article-title":"Efficient estimation in the errors-in-variables model","volume":"15","author":"Bickel","year":"1987","journal-title":"Ann. 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