{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T00:17:11Z","timestamp":1725668231382},"reference-count":15,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2021,8,19]],"date-time":"2021-08-19T00:00:00Z","timestamp":1629331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,8,24]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>The three-parameter generalized extreme value distribution arises from classical univariate extreme value theory, and is in common use for analysing the far tail of observed phenomena, yet important asymptotic properties of likelihood-based estimation under this standard model have not been established. In this paper we prove that the maximum likelihood estimator is global and unique. An interesting secondary result entails the uniform consistency of a class of limit relations in a tight neighbourhood of the true shape parameter.<\/jats:p>","DOI":"10.1093\/biomet\/asab043","type":"journal-article","created":{"date-parts":[[2021,8,17]],"date-time":"2021-08-17T20:24:39Z","timestamp":1629231879000},"page":"853-864","source":"Crossref","is-referenced-by-count":2,"title":["Uniqueness and global optimality of the maximum likelihood estimator for the generalized extreme value distribution"],"prefix":"10.1093","volume":"109","author":[{"given":"Likun","family":"Zhang","sequence":"first","affiliation":[{"name":"Climate and Ecosystem Sciences Division, Lawrence Berkeley National Laboratory , Berkeley, California 94720, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benjamin A","family":"Shaby","sequence":"additional","affiliation":[{"name":"Department of Statistics, Colorado State University , Fort Collins, Colorado 80523, U.S.A"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2021,8,19]]},"reference":[{"key":"2022082420280724600_B1","doi-asserted-by":"crossref","DOI":"10.1002\/0470012382","volume-title":"Statistics of Extremes","author":"Beirlant,","year":"2004"},{"key":"2022082420280724600_B2","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/S0169-7161(05)25002-2","article-title":"Reference analysis","volume-title":"Bayesian Thinking: Modeling and Computation","author":"Bernardo,","year":"2005"},{"key":"2022082420280724600_B3","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1007\/s10687-017-0292-6","article-title":"On the maximum likelihood estimator for the generalized extreme-value distribution","volume":"20","author":"B\u00fccher,","year":"2017","journal-title":"Extremes"},{"key":"2022082420280724600_B4","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1111\/j.2517-6161.1985.tb01384.x","article-title":"On asymptotic normality of limiting density functions with Bayesian implications","volume":"47","author":"Chen,","year":"1985","journal-title":"J. R. Statist. Soc."},{"key":"2022082420280724600_B5","first-page":"372","article-title":"Large sample theory for fitting an approximating Gumbel model to maxima","volume":"48","author":"Cohen,","year":"1986","journal-title":"Sankhy\u0101 Ser. A"},{"key":"2022082420280724600_B6","first-page":"74","article-title":"Fitting extreme value distributions to maxima","volume":"50","author":"Cohen,","year":"1988","journal-title":"Sankhy\u0101 Ser. A"},{"key":"2022082420280724600_B7","doi-asserted-by":"crossref","first-page":"420","DOI":"10.3150\/13-BEJ573","article-title":"Existence and consistency of the maximum likelihood estimators for the extreme value index within the block maxima framework","volume":"21","author":"Dombry,","year":"2015","journal-title":"Bernoulli"},{"key":"2022082420280724600_B8","doi-asserted-by":"crossref","first-page":"1690","DOI":"10.3150\/18-BEJ1032","article-title":"Maximum likelihood estimators based on the block maxima method","volume":"25","author":"Dombry,","year":"2019","journal-title":"Bernoulli"},{"key":"2022082420280724600_B9","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1017\/S0305004100015681","article-title":"Limiting forms of the frequency distribution of the largest or smallest member of a sample","volume":"24","author":"Fisher,","year":"1928","journal-title":"Math. Proc. Camb. Phil. Soc."},{"key":"2022082420280724600_B10","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8242-3","volume-title":"Bayes Theory","author":"Hartigan,","year":"1983"},{"key":"2022082420280724600_B11","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1080\/00401706.1985.10488049","article-title":"Estimation of the generalized extreme-value distribution by the method of probability-weighted moments","volume":"27","author":"Hosking,","year":"1985","journal-title":"Technometrics"},{"key":"2022082420280724600_B12","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1029\/96WR03848","article-title":"Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events: 1. At-site modeling","volume":"33","author":"Madsen,","year":"1997","journal-title":"Water Resources Res."},{"key":"2022082420280724600_B13","first-page":"119","article-title":"Statistical inference using extreme order statistics","volume":"3","author":"Pickands,","year":"1975","journal-title":"Ann. Statist."},{"key":"2022082420280724600_B14","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1093\/biomet\/72.1.67","article-title":"Maximum likelihood estimation in a class of nonregular cases","volume":"72","author":"Smith,","year":"1985","journal-title":"Biometrika"},{"volume-title":"Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik","year":"1931","author":"von Mises,","key":"2022082420280724600_B15"}],"container-title":["Biometrika"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/biomet\/advance-article-pdf\/doi\/10.1093\/biomet\/asab043\/41382516\/asab043.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/109\/3\/853\/45512169\/asab043.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/biomet\/article-pdf\/109\/3\/853\/45512169\/asab043.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T19:09:00Z","timestamp":1725649740000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/biomet\/article\/109\/3\/853\/6355019"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,19]]},"references-count":15,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,8,19]]},"published-print":{"date-parts":[[2022,8,24]]}},"URL":"https:\/\/doi.org\/10.1093\/biomet\/asab043","relation":{},"ISSN":["0006-3444","1464-3510"],"issn-type":[{"type":"print","value":"0006-3444"},{"type":"electronic","value":"1464-3510"}],"subject":[],"published-other":{"date-parts":[[2022,9,1]]},"published":{"date-parts":[[2021,8,19]]}}}