Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/33024 https://doi.org/Caeiro, F, Henriques-Rodrigues, L, Gomes, MI, Cabral, I. Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study. Comp and Math Methods. 2020; 2:e1101. https://doi.org/10.1002/cmm4.1101 https://doi.org/10.1002/cmm4.1101 |
Resumo: | In extreme value (EV) analysis, the EV index (EVI), , is the primary parame- ter of extreme events. In this work, we consider positive, that is, we assume that F is heavy tailed. Classical tail parameters estimators, such as the Hill, the Moments, or the Weissman estimators, are usually asymptotically biased. Con- sequently, those estimators are quite sensitive to the number of upper order statistics used in the estimation. Minimum-variance reduced-bias (RB) estima- tors have enabled us to remove the dominant component of asymptotic bias without increasing the asymptotic variance of the new estimators. The purpose of this paper is to study a new minimum-variance RB estimator of the EVI. Under adequate conditions, we prove their nondegenerate asymptotic behavior. More- over, an asymptotic and empirical comparison with other minimum-variance RB estimators from the literature is also provided. Our results show that the proposed new estimator has the potential to be very useful in practice. |
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Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical studyasymptotic biasextreme value indexminimum asymptotic biassemiparametric estimationstatistic of extremesIn extreme value (EV) analysis, the EV index (EVI), , is the primary parame- ter of extreme events. In this work, we consider positive, that is, we assume that F is heavy tailed. Classical tail parameters estimators, such as the Hill, the Moments, or the Weissman estimators, are usually asymptotically biased. Con- sequently, those estimators are quite sensitive to the number of upper order statistics used in the estimation. Minimum-variance reduced-bias (RB) estima- tors have enabled us to remove the dominant component of asymptotic bias without increasing the asymptotic variance of the new estimators. The purpose of this paper is to study a new minimum-variance RB estimator of the EVI. Under adequate conditions, we prove their nondegenerate asymptotic behavior. More- over, an asymptotic and empirical comparison with other minimum-variance RB estimators from the literature is also provided. Our results show that the proposed new estimator has the potential to be very useful in practice.Wiley / Computational and Mathematical Methods2022-12-29T16:49:19Z2022-12-292020-03-26T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/33024https://doi.org/Caeiro, F, Henriques-Rodrigues, L, Gomes, MI, Cabral, I. Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study. Comp and Math Methods. 2020; 2:e1101. https://doi.org/10.1002/cmm4.1101http://hdl.handle.net/10174/33024https://doi.org/10.1002/cmm4.1101enghttps://onlinelibrary.wiley.com/doi/full/10.1002/cmm4.1101Computational and Mathematical Methodsfac@fct.unl.ptligiahr@uevora.ptmigomes@fc.ul.ptnd336Caeiro, FredericoHenriques-Rodrigues, LígiaGomes, M. IvetteCabral, Ivanildainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-03T19:34:16Zoai:dspace.uevora.pt:10174/33024Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:21:54.114124Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study |
title |
Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study |
spellingShingle |
Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study Caeiro, Frederico asymptotic bias extreme value index minimum asymptotic bias semiparametric estimation statistic of extremes |
title_short |
Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study |
title_full |
Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study |
title_fullStr |
Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study |
title_full_unstemmed |
Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study |
title_sort |
Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study |
author |
Caeiro, Frederico |
author_facet |
Caeiro, Frederico Henriques-Rodrigues, Lígia Gomes, M. Ivette Cabral, Ivanilda |
author_role |
author |
author2 |
Henriques-Rodrigues, Lígia Gomes, M. Ivette Cabral, Ivanilda |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Caeiro, Frederico Henriques-Rodrigues, Lígia Gomes, M. Ivette Cabral, Ivanilda |
dc.subject.por.fl_str_mv |
asymptotic bias extreme value index minimum asymptotic bias semiparametric estimation statistic of extremes |
topic |
asymptotic bias extreme value index minimum asymptotic bias semiparametric estimation statistic of extremes |
description |
In extreme value (EV) analysis, the EV index (EVI), , is the primary parame- ter of extreme events. In this work, we consider positive, that is, we assume that F is heavy tailed. Classical tail parameters estimators, such as the Hill, the Moments, or the Weissman estimators, are usually asymptotically biased. Con- sequently, those estimators are quite sensitive to the number of upper order statistics used in the estimation. Minimum-variance reduced-bias (RB) estima- tors have enabled us to remove the dominant component of asymptotic bias without increasing the asymptotic variance of the new estimators. The purpose of this paper is to study a new minimum-variance RB estimator of the EVI. Under adequate conditions, we prove their nondegenerate asymptotic behavior. More- over, an asymptotic and empirical comparison with other minimum-variance RB estimators from the literature is also provided. Our results show that the proposed new estimator has the potential to be very useful in practice. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-03-26T00:00:00Z 2022-12-29T16:49:19Z 2022-12-29 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10174/33024 https://doi.org/Caeiro, F, Henriques-Rodrigues, L, Gomes, MI, Cabral, I. Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study. Comp and Math Methods. 2020; 2:e1101. https://doi.org/10.1002/cmm4.1101 http://hdl.handle.net/10174/33024 https://doi.org/10.1002/cmm4.1101 |
url |
http://hdl.handle.net/10174/33024 https://doi.org/Caeiro, F, Henriques-Rodrigues, L, Gomes, MI, Cabral, I. Minimum-variance reduced-bias estimation of the extreme value index: A theoretical and empirical study. Comp and Math Methods. 2020; 2:e1101. https://doi.org/10.1002/cmm4.1101 https://doi.org/10.1002/cmm4.1101 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://onlinelibrary.wiley.com/doi/full/10.1002/cmm4.1101 Computational and Mathematical Methods fac@fct.unl.pt ligiahr@uevora.pt migomes@fc.ul.pt nd 336 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Wiley / Computational and Mathematical Methods |
publisher.none.fl_str_mv |
Wiley / Computational and Mathematical Methods |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
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1799136700627156992 |