{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T14:14:56Z","timestamp":1792678496908,"version":"4.5.0"},"reference-count":31,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T00:00:00Z","timestamp":1762300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,2,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We provide finite-sample distribution approximations that are uniform in the parameter for inference in linear mixed models. The focus is on variances and covariances of random effects in cases where existing theory fails because the covariance matrix is nearly or exactly singular and hence near or at the boundary of the parameter set. Quantitative bounds on the differences between the standard normal density and densities of linear combinations of the score function enable, for example, the assessment of sufficient sample size. The bounds also lead to useful asymptotic theory in settings where both the number of parameters and the number of random effects grow with the sample size. We consider models with independent clusters and ones with a possibly diverging number of crossed random effects, which are notoriously complicated. Simulations indicate that the theory leads to practically relevant methods. In particular, the studied confidence regions, which are straightforward to implement, have near-nominal coverage in finite samples even when some random effects have variances near or equal to zero, or have correlations near or equal to $ \\pm 1 $.<\/jats:p>","DOI":"10.1093\/biomet\/asaf079","type":"journal-article","created":{"date-parts":[[2025,11,9]],"date-time":"2025-11-09T01:35:21Z","timestamp":1762652121000},"source":"Crossref","is-referenced-by-count":3,"title":["Uniform inference in linear mixed models"],"prefix":"10.1093","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8085-4353","authenticated-orcid":false,"given":"Karl Oskar","family":"Ekvall","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Florida , 102 Griffin-Floyd Hall , Gainesville, Florida 32611, U.S.A. k.ekvall@ufl.edu"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matteo","family":"Bottai","sequence":"additional","affiliation":[{"name":"Division of Biostatistics, Institute of Environmental Medicine, Karolinska Institute , 171 77 Stockholm, \u00a0 matteo.bottai@ki.se","place":["Sweden"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,11,5]]},"reference":[{"key":"2026032607092977000_asaf079-B1","first-page":"27","article-title":"Fitting linear mixed models in R","volume":"5","author":"Bates","year":"2005","journal-title":"R News"},{"key":"2026032607092977000_asaf079-B2","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1093\/biomet\/asad044","article-title":"An anomaly arising in the analysis of processes with more than one source of variability","volume":"111","author":"Battey","year":"2024","journal-title":"Biometrika"},{"key":"2026032607092977000_asaf079-B3","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1093\/biomet\/90.1.73","article-title":"Confidence regions when the Fisher information is zero","volume":"90","author":"Bottai","year":"2003","journal-title":"Biometrika"},{"key":"2026032607092977000_asaf079-B4","doi-asserted-by":"crossref","first-page":"865","DOI":"10.2307\/1911188","article-title":"Testing for neglected heterogeneity","volume":"52","author":"Chesher","year":"1984","journal-title":"Econometrica"},{"key":"2026032607092977000_asaf079-B5","volume-title":"Theoretical Statistics","author":"Cox","year":"2000"},{"key":"2026032607092977000_asaf079-B6","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1111\/j.1467-9868.2004.00438.x","article-title":"Likelihood ratio tests in linear mixed models with one variance component","volume":"66","author":"Crainiceanu","year":"2004","journal-title":"J. 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