{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,27]],"date-time":"2026-09-27T04:54:39Z","timestamp":1790484879997,"version":"4.1.0"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2014,12,13]],"date-time":"2014-12-13T00:00:00Z","timestamp":1418428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Desenvolvimento de Extremos no Tempo a no Espa\u00e7o","award":["EXPL\/MAT-STA\/0622\/2013"],"award-info":[{"award-number":["EXPL\/MAT-STA\/0622\/2013"]}]},{"name":"national funds","award":["PEst-OE\/MAT\/UI0006\/2014"],"award-info":[{"award-number":["PEst-OE\/MAT\/UI0006\/2014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,1,1]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We extend classical extreme value theory to non-identically distributed observations. When the tails of the distribution are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated non-parametrically along with the (common) extreme value index. For a positive extreme value index, joint asymptotic normality of both estimators is shown; they are asymptotically independent. We also establish asymptotic normality of a forecasted high quantile and develop tests for the proportionality function and for the validity of the model. We show through simulations the good performance of the procedures and also present an application to stock market returns. A main tool is the weak convergence of a weighted sequential tail empirical process.<\/jats:p>","DOI":"10.1111\/rssb.12099","type":"journal-article","created":{"date-parts":[[2014,12,13]],"date-time":"2014-12-13T01:05:34Z","timestamp":1418432734000},"page":"31-51","source":"Crossref","is-referenced-by-count":84,"title":["Statistics of Heteroscedastic Extremes"],"prefix":"10.1093","volume":"78","author":[{"given":"John H. J.","family":"Einmahl","sequence":"first","affiliation":[{"name":"Tilburg University , The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laurens","family":"Haan","sequence":"additional","affiliation":[{"name":"Erasmus University Rotterdam , The Netherlands"},{"name":"University of Lisbon , Portugal"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chen","family":"Zhou","sequence":"additional","affiliation":[{"name":"De Nederlandsche Bank , Amsterdam"},{"name":"Erasmus University Rotterdam , The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2014,12,13]]},"reference":[{"key":"2023021709312317400_rssb12099-cit-0001","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-3675-0","volume-title":"An Introduction to Statistical Modeling of Extreme Values","author":"Coles","year":"2001"},{"key":"2023021709312317400_rssb12099-cit-0002","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1111\/j.2517-6161.1990.tb01796.x","article-title":"Models for exceedances over high thresholds (with discussion)","volume":"52","author":"Davison","year":"1990","journal-title":"J. R. Statist. Soc. B"},{"key":"2023021709312317400_rssb12099-cit-0003","doi-asserted-by":"crossref","first-page":"1274","DOI":"10.1214\/aoap\/1019487617","article-title":"Weighted approximations of tail processes for \u03b2-mixing random variables","volume":"10","author":"Drees","year":"2000","journal-title":"Ann. Appl. Probab."},{"key":"2023021709312317400_rssb12099-cit-0004","doi-asserted-by":"crossref","first-page":"2145","DOI":"10.1214\/09-AOS788","article-title":"Limit theorems for empirical processes of cluster functionals","volume":"38","author":"Drees","year":"2010","journal-title":"Ann. Statist."},{"key":"2023021709312317400_rssb12099-cit-0005","doi-asserted-by":"crossref","first-page":"3003","DOI":"10.1016\/j.jspi.2010.03.041","article-title":"Asymptotics of the shorth plot","volume":"140","author":"Einmahl","year":"2010","journal-title":"J. Statist. Planng Inf."},{"key":"2023021709312317400_rssb12099-cit-0006","doi-asserted-by":"crossref","DOI":"10.1007\/0-387-34471-3","volume-title":"Extreme Value Theory: an Introduction","author":"Haan","year":"2006"},{"key":"2023021709312317400_rssb12099-cit-0007","volume-title":"On tail trend detection: modeling relative risk","author":"Haan","year":"2014"},{"key":"2023021709312317400_rssb12099-cit-0008","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1017\/S144678870000046X","article-title":"Generalized regular variation of second order","volume":"61","author":"Haan","year":"1996","journal-title":"J. Aust. Math. Soc. A"},{"key":"2023021709312317400_rssb12099-cit-0009","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1214\/ss\/1009212755","article-title":"Nonparametric analysis of temporal trend when fitting parametric models to extreme-value data","volume":"15","author":"Hall","year":"2000","journal-title":"Statist. 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