{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T14:35:30Z","timestamp":1774622130883,"version":"3.50.1"},"reference-count":47,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T00:00:00Z","timestamp":1646870400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/0006\/2020"],"award-info":[{"award-number":["UIDB\/0006\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04674\/2020"],"award-info":[{"award-number":["UIDB\/04674\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods"],"published-print":{"date-parts":[[2022,3,10]]},"abstract":"<jats:p>The Box-Cox transformations are used to make the data more suitable for statistical analysis. We know from the literature that this transformation of the data can increase the rate of convergence of the tail of the distribution to the generalized extreme value distribution, and as a byproduct, the bias of the estimation procedure is reduced. The reduction of bias of the Hill estimator has been widely addressed in the literature of extreme value theory. Several techniques have been used to achieve such reduction of bias, either by removing the main component of the bias of the Hill estimator of the extreme value index (EVI) or by constructing new estimators based on generalized means or norms that generalize the Hill estimator. We are going to study the Box-Cox Hill estimator introduced by Teugels and Vanroelen, in 2004, proving the consistency and asymptotic normality of the estimator and addressing the choice and estimation of the power and shift parameters of the Box-Cox transformation for the EVI estimation. The performance of the estimators under study will be illustrated for finite samples through small-scale Monte Carlo simulation studies.<\/jats:p>","DOI":"10.1155\/2022\/3854763","type":"journal-article","created":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T20:05:07Z","timestamp":1646942707000},"page":"1-15","source":"Crossref","is-referenced-by-count":3,"title":["Box-Cox Transformations and Bias Reduction in Extreme Value Theory"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4881-4188","authenticated-orcid":true,"given":"L\u00edgia","family":"Henriques-Rodrigues","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Science and Technology, University of \u00c9vora, \u00c9vora, Portugal"},{"name":"Research Center in Mathematics and Applications (CIMA), University of \u00c9vora, \u00c9vora, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2903-6993","authenticated-orcid":true,"given":"M. Ivette","family":"Gomes","sequence":"additional","affiliation":[{"name":"DEIO, Faculty of Sciences, University of Lisbon (FCUL), Lisbon, Portugal"},{"name":"Statistics and Applications Center (CEAUL), University of Lisbon, Lisbon, Portugal"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1964.tb00553.x"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1765(03)00035-1"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1082552200"},{"key":"4","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0079658","volume-title":"Regularly Varying Functions","author":"E. Seneta","year":"1976"},{"key":"5","volume-title":"Regular Variation","author":"N. H. Bingham","year":"1989"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9876.2008.00638.x"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOAS333"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s10986-013-9212-x"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/s10463-015-0548-3"},{"key":"10","volume-title":"Slow Variation and Characterization of Domains of Attraction","author":"L. de Haan","year":"1984"},{"key":"11","volume-title":"Regular Variation, Extensions and Tauberian Theorems","author":"J. Geluk","year":"1987"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176346596"},{"key":"13","doi-asserted-by":"crossref","DOI":"10.1007\/0-387-34471-3","volume-title":"Extreme Value Theory: An Introduction","author":"L. de Haan","year":"2006"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176343247"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-7152(97)00160-0"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009975020370"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1018031215"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1023\/a:1011470010228"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1111\/insr.12058"},{"issue":"2","key":"20","first-page":"113","article-title":"Direct reduction of bias of the classical Hill estimator","volume":"3","author":"F. Caeiro","year":"2005","journal-title":"Revstat - Statistical Journal"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1080\/03610920802361415"},{"issue":"2","key":"22","first-page":"177","article-title":"Improving second order reduced bias extreme value index estimation","volume":"5","author":"M. I. Gomes","year":"2007","journal-title":"Revstat - Statistical Journal"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2007.00620.x"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1198\/016214506000000799"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2012.07.019"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1007\/s10687-016-0261-5"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1002\/cmm4.1025"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1002\/cmm4.1101"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1002\/cmm4.1167"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1007\/s10463-013-0412-2"},{"issue":"1","key":"31","first-page":"91","article-title":"Using shrinkage estimators to reduce bias and MSE in estimation of heavy tails","volume":"17","author":"J. Beirlant","year":"2019","journal-title":"Revstat - Statistical Journal"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9574.00068"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1081\/SAC-120023875"},{"issue":"2","key":"34","first-page":"193","article-title":"A new class of semi-parametric estimators of the second order parameter","volume":"60","author":"M. I. Fraga Alves","year":"2003","journal-title":"Portugali\u00e6 Mathematica"},{"key":"35","doi-asserted-by":"publisher","DOI":"10.1007\/s10687-006-0026-7"},{"key":"36","doi-asserted-by":"publisher","DOI":"10.1023\/A:1020925908039"},{"key":"37","doi-asserted-by":"publisher","DOI":"10.1007\/s11749-008-0108-8"},{"key":"38","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2010.03.029"},{"key":"39","doi-asserted-by":"publisher","DOI":"10.1007\/s10687-009-0086-6"},{"key":"40","doi-asserted-by":"publisher","DOI":"10.1051\/ps\/2010017"},{"key":"41","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2011.11.016"},{"issue":"3","key":"42","first-page":"299","article-title":"PORT-estimation of a shape second-order parameter","volume":"12","author":"L. Henriques-Rodrigues","year":"2014","journal-title":"Revstat - Statistical Journal"},{"key":"43","doi-asserted-by":"publisher","DOI":"10.1080\/00949650902755178"},{"key":"44","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1982.tb01183.x"},{"key":"45","doi-asserted-by":"publisher","DOI":"10.1081\/SAC-100107790"},{"key":"46","first-page":"3590","article-title":"The link between the excesses over a high threshold and the shifted Hill estimator","volume":"LXII","author":"M. I. Gomes","year":"2007","journal-title":"Bulletin of the International Statistical Institute (ISI)"},{"key":"47","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016592028871"}],"container-title":["Computational and Mathematical Methods"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmm\/2022\/3854763.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmm\/2022\/3854763.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmm\/2022\/3854763.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T20:05:22Z","timestamp":1646942722000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/cmm\/2022\/3854763\/"}},"subtitle":[],"editor":[{"given":"Christophe","family":"Chesneau","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2022,3,10]]},"references-count":47,"alternative-id":["3854763","3854763"],"URL":"https:\/\/doi.org\/10.1155\/2022\/3854763","relation":{},"ISSN":["2577-7408"],"issn-type":[{"value":"2577-7408","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,10]]}}}