{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T16:03:06Z","timestamp":1789228986434,"version":"build-2803163510"},"reference-count":31,"publisher":"The Econometric Society","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>This paper presents finite\u2010sample efficiency bounds for the core econometric problem of estimation of linear regression coefficients. We show that the classical Gauss\u2013Markov theorem can be restated omitting the unnatural restriction to linear estimators, without adding any extra conditions. Our results are lower bounds on the variances of unbiased estimators. These lower bounds correspond to the variances of the the least squares estimator and the generalized least squares estimator, depending on the assumption on the error covariances. These results show that we can drop the label \u201clinear estimator\u201d from the pedagogy of the Gauss\u2013Markov theorem. Instead of referring to these estimators as BLUE, they can legitimately be called BUE (best unbiased estimators).<\/jats:p>","DOI":"10.3982\/ecta19255","type":"journal-article","created":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T13:12:32Z","timestamp":1653484352000},"page":"1283-1294","source":"Crossref","is-referenced-by-count":38,"title":["A Modern Gauss\u2013Markov Theorem"],"prefix":"10.3982","volume":"90","author":[{"given":"Bruce E.","family":"Hansen","sequence":"first","affiliation":[{"name":"Department of Economics, University of Wisconsin"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2022]]},"reference":[{"key":"ecta200398-bib-0001","first-page":"42","volume":"55","author":"Aitken","year":"1935","journal-title":"Proceedings of the Royal Statistical Society"},{"key":"ecta200398-bib-0002","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1214\/aos\/1176346151","volume":"11","author":"Begun","year":"1983","journal-title":"The Annals of Statistics"},{"key":"ecta200398-bib-0003","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/0047-259X(89)90038-9","volume":"3","author":"Berk","year":"1989","journal-title":"Journal of Multivariate Analysis"},{"issue":"3","key":"ecta200398-bib-0004","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1214\/aos\/1176345863","volume":"10","author":"Bickel","year":"1982","journal-title":"Annals of Statistics"},{"key":"ecta200398-bib-0005","volume-title":"Efficient and Adaptive Estimation for Semiparametric Models","author":"Bickel","year":"1993"},{"key":"ecta200398-bib-0006","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/0304-4076(87)90015-7","volume":"34","author":"Chamberlain","year":"1987","journal-title":"Journal of Econometrics"},{"key":"ecta200398-bib-0007","first-page":"440","volume":"17","author":"Doss","year":"1989","journal-title":"The Annals of Statistics"},{"key":"ecta200398-bib-0008","volume-title":"Theoria Motus Corporum Celestium","author":"Gauss","year":"1809"},{"key":"ecta200398-bib-0009","volume-title":"Theoria Comationis Observationum Erroribus Minimis Obnoxiae","author":"Gauss","year":"1823"},{"key":"ecta200398-bib-0010","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1080\/02331889208802348","volume":"23","author":"Gnot","year":"1992","journal-title":"Statistics"},{"key":"ecta200398-bib-0011","first-page":"175","volume-title":"Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability","volume":"1","author":"Hajek","year":"1972"},{"key":"ecta200398-bib-0012","doi-asserted-by":"crossref","unstructured":"Hansen, Bruce E. 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