{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:36:46Z","timestamp":1791333406940,"version":"4.3.1"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,4,8]],"date-time":"2023-04-08T00:00:00Z","timestamp":1680912000000},"content-version":"vor","delay-in-days":7375,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS 9870193"],"award-info":[{"award-number":["DMS 9870193"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003,2,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The paper considers a rectangular array asymptotic embedding for multistratum data sets, in which both the number of strata and the number of within-stratum replications increase, and at the same rate. It is shown that under this embedding the maximum likelihood estimator is consistent but not efficient owing to a non-zero mean in its asymptotic normal distribution. By using a projection operator on the score function, an adjusted maximum likelihood estimator can be obtained that is asymptotically unbiased and has a variance that attains the Cram\u00e9r\u2013Rao lower bound. The adjusted maximum likelihood estimator can be viewed as an approximation to the conditional maximum likelihood estimator.<\/jats:p>","DOI":"10.1111\/1467-9868.00380","type":"journal-article","created":{"date-parts":[[2003,3,12]],"date-time":"2003-03-12T19:37:44Z","timestamp":1047497864000},"page":"191-208","source":"Crossref","is-referenced-by-count":24,"title":["Efficiency of Projected Score Methods in Rectangular Array Asymptotics"],"prefix":"10.1093","volume":"65","author":[{"given":"Haihong","family":"Li","sequence":"first","affiliation":[{"name":"Frontier Science and Technology Research Foundation , Chestnut Hill , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bruce G.","family":"Lindsay","sequence":"additional","affiliation":[{"name":"Pennsylvania State University , University Park , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard P.","family":"Waterman","sequence":"additional","affiliation":[{"name":"University of Pennsylvania , Philadelphia , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2003,1,28]]},"reference":[{"key":"2023040900081458300_","first-page":"78","article-title":"On Fisher's lower bound to asymptotic variances in case of infinitely many nuisance parameters","volume":"53","author":"Andersen","year":"1970","journal-title":"Skand. 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