{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T07:37:55Z","timestamp":1785569875146,"version":"3.56.0"},"reference-count":5,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T00:00:00Z","timestamp":1700092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A recent article by Jiang et\u00a0al. (2022) on generalized linear mixed model asymptotics derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If m denotes the number of groups and n is the average within-group sample size then the asymptotic variances have orders m\u22121 and (mn)\u22121, depending on the parameter. We extend this theory to provide explicit forms of the (mn)\u22121 second terms of the asymptotically harder-to-estimate parameters. Improved accuracy of statistical inference and planning are consequences of our theory.<\/jats:p>","DOI":"10.1093\/biomet\/asad072","type":"journal-article","created":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T18:13:34Z","timestamp":1700158414000},"page":"1077-1084","source":"Crossref","is-referenced-by-count":3,"title":["Second term improvement to generalized linear mixed model asymptotics"],"prefix":"10.1093","volume":"111","author":[{"given":"Luca","family":"Maestrini","sequence":"first","affiliation":[{"name":"Research School of Finance, Actuarial Studies and Statistics, The Australian National University , Kingsley Street , Canberra 2601, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aishwarya","family":"Bhaskaran","sequence":"additional","affiliation":[{"name":"School of Mathematical and Physical Sciences, University of Technology Sydney , P.O. Box 123 , Broadway 2007, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2555-896X","authenticated-orcid":false,"given":"Matt P","family":"Wand","sequence":"additional","affiliation":[{"name":"School of Mathematical and Physical Sciences, University of Technology Sydney , P.O. Box 123 , Broadway 2007, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,11,16]]},"reference":[{"key":"2024090418511527700_asad072-B1","doi-asserted-by":"crossref","first-page":"109691","DOI":"10.1016\/j.spl.2022.109691","article-title":"Dispersion parameter extension of precise generalized linear mixed model asymptotics","volume":"193","author":"Bhaskaran","year":"2023","journal-title":"Statist. Prob. Lett"},{"key":"2024090418511527700_asad072-B2","author":"Brooks","year":"2023"},{"key":"2024090418511527700_asad072-B3","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1111\/rssb.12473","article-title":"Usable and precise asymptotics for generalized linear mixed model analysis and design","volume":"84","author":"Jiang","year":"2022","journal-title":"J. R. Statist. Soc. B"},{"key":"2024090418511527700_asad072-B4","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.jspi.2021.07.009","article-title":"Increasing cluster size asymptotics for nested error regression models","volume":"217","author":"Lyu","year":"2022","journal-title":"J. Statist. Plan. 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