Peaks over random threshold methodology for tail index and high quantile estimation
Autor(a) principal: | |
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Data de Publicação: | 2006 |
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/10400.15/123 |
Resumo: | In this paper we present a class of semi-parametric high quantile estimators which enjoy a desirable property in the presence of linear transformations of the data. Such a feature is in accordance with the empirical counterpart of the theoretical linearity of a quantile χp: χp(δX + λ) = δχp(X) + λ, for any real λ and positive δ. This class of estimators is based on the sample of excesses over a random threshold, originating what we denominate PORT (Peaks Over Random Threshold) methodology. We prove consistency and asymptotic normality of two high quantile estimators in this class, associated with the PORT-estimators for the tail index. The exact performance of the new tail index and quantile PORT-estimators is compared with the original semiparametric estimators, through a simulation study. |
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Peaks over random threshold methodology for tail index and high quantile estimationHeavy tailsHigh quantilesSemi-parametric estimationLinear propertySample of excessesIn this paper we present a class of semi-parametric high quantile estimators which enjoy a desirable property in the presence of linear transformations of the data. Such a feature is in accordance with the empirical counterpart of the theoretical linearity of a quantile χp: χp(δX + λ) = δχp(X) + λ, for any real λ and positive δ. This class of estimators is based on the sample of excesses over a random threshold, originating what we denominate PORT (Peaks Over Random Threshold) methodology. We prove consistency and asymptotic normality of two high quantile estimators in this class, associated with the PORT-estimators for the tail index. The exact performance of the new tail index and quantile PORT-estimators is compared with the original semiparametric estimators, through a simulation study.Instituto Nacional de EstatísticaRepositório Científico do Instituto Politécnico de SantarémSantos, Paulo AraújoAlves, M. Isabel FragaGomes, M. Ivette2010-07-09T13:34:33Z2006-112006-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.15/123engSANTOS, Paulo Araújo ; ALVES, M. Isabel Fraga ; GOMES, M. Ivette - Peaks over random threshold methodology for tail index and high quantile estimation. Revstat. ISSN 1645-6726. Vol. 4, no. 3 (Nov. 2006), p. 227-2471645-6726info: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:RCAAP2024-01-21T07:28:39Zoai:repositorio.ipsantarem.pt:10400.15/123Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:52:49.277842Repositório 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 |
Peaks over random threshold methodology for tail index and high quantile estimation |
title |
Peaks over random threshold methodology for tail index and high quantile estimation |
spellingShingle |
Peaks over random threshold methodology for tail index and high quantile estimation Santos, Paulo Araújo Heavy tails High quantiles Semi-parametric estimation Linear property Sample of excesses |
title_short |
Peaks over random threshold methodology for tail index and high quantile estimation |
title_full |
Peaks over random threshold methodology for tail index and high quantile estimation |
title_fullStr |
Peaks over random threshold methodology for tail index and high quantile estimation |
title_full_unstemmed |
Peaks over random threshold methodology for tail index and high quantile estimation |
title_sort |
Peaks over random threshold methodology for tail index and high quantile estimation |
author |
Santos, Paulo Araújo |
author_facet |
Santos, Paulo Araújo Alves, M. Isabel Fraga Gomes, M. Ivette |
author_role |
author |
author2 |
Alves, M. Isabel Fraga Gomes, M. Ivette |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Repositório Científico do Instituto Politécnico de Santarém |
dc.contributor.author.fl_str_mv |
Santos, Paulo Araújo Alves, M. Isabel Fraga Gomes, M. Ivette |
dc.subject.por.fl_str_mv |
Heavy tails High quantiles Semi-parametric estimation Linear property Sample of excesses |
topic |
Heavy tails High quantiles Semi-parametric estimation Linear property Sample of excesses |
description |
In this paper we present a class of semi-parametric high quantile estimators which enjoy a desirable property in the presence of linear transformations of the data. Such a feature is in accordance with the empirical counterpart of the theoretical linearity of a quantile χp: χp(δX + λ) = δχp(X) + λ, for any real λ and positive δ. This class of estimators is based on the sample of excesses over a random threshold, originating what we denominate PORT (Peaks Over Random Threshold) methodology. We prove consistency and asymptotic normality of two high quantile estimators in this class, associated with the PORT-estimators for the tail index. The exact performance of the new tail index and quantile PORT-estimators is compared with the original semiparametric estimators, through a simulation study. |
publishDate |
2006 |
dc.date.none.fl_str_mv |
2006-11 2006-11-01T00:00:00Z 2010-07-09T13:34:33Z |
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/10400.15/123 |
url |
http://hdl.handle.net/10400.15/123 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
SANTOS, Paulo Araújo ; ALVES, M. Isabel Fraga ; GOMES, M. Ivette - Peaks over random threshold methodology for tail index and high quantile estimation. Revstat. ISSN 1645-6726. Vol. 4, no. 3 (Nov. 2006), p. 227-247 1645-6726 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Instituto Nacional de Estatística |
publisher.none.fl_str_mv |
Instituto Nacional de Estatística |
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 |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
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RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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