A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic

Detalhes bibliográficos
Autor(a) principal: Arendarczyk , Marek
Data de Publicação: 2023
Outros Autores: J. Kozubowski , Tomasz, K. Panorska , Anna
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://doi.org/10.57805/revstat.v21i3.357
Resumo: The generalized Pareto distributions (GPDs) play an important role in the statistics of extremes. We point various problems with the likelihood-based inference for the index parameter α of the GPDs, and develop alternative testing strategies, which do not require parameter estimation. Our test statistic is the Greenwood statistic, which probability distribution is stochastically increasing with respect to α within the GPDs. We compare the performance of our test to a test with maximum-to-sum ratio test statistic Rn. New results on the properties of the Rn are also presented, as well as recommendations for calculating the p-values and illustrative data examples.
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spelling A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statisticcoefficient of variationextremesgeneralized Pareto distributionheavy tailed distributionpower lawPeak-over-thresholdThe generalized Pareto distributions (GPDs) play an important role in the statistics of extremes. We point various problems with the likelihood-based inference for the index parameter α of the GPDs, and develop alternative testing strategies, which do not require parameter estimation. Our test statistic is the Greenwood statistic, which probability distribution is stochastically increasing with respect to α within the GPDs. We compare the performance of our test to a test with maximum-to-sum ratio test statistic Rn. New results on the properties of the Rn are also presented, as well as recommendations for calculating the p-values and illustrative data examples.Statistics Portugal2023-07-31info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://doi.org/10.57805/revstat.v21i3.357https://doi.org/10.57805/revstat.v21i3.357REVSTAT-Statistical Journal; Vol. 21 No. 3 (2023): REVSTAT-Statistical Journal; 367–388REVSTAT; Vol. 21 N.º 3 (2023): REVSTAT-Statistical Journal; 367–3882183-03711645-6726reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAPenghttps://revstat.ine.pt/index.php/REVSTAT/article/view/357https://revstat.ine.pt/index.php/REVSTAT/article/view/357/651https://revstat.ine.pt/index.php/REVSTAT/article/view/357/540Copyright (c) 2022 REVSTAT-Statistical Journalinfo:eu-repo/semantics/openAccessArendarczyk , MarekJ. Kozubowski , TomaszK. Panorska , Anna2023-08-12T06:30:22Zoai:revstat:article/357Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:26:50.200330Repositório 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 A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic
title A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic
spellingShingle A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic
Arendarczyk , Marek
coefficient of variation
extremes
generalized Pareto distribution
heavy tailed distribution
power law
Peak-over-threshold
title_short A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic
title_full A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic
title_fullStr A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic
title_full_unstemmed A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic
title_sort A Computational Approach to Confidence Intervals and Testing for Generalized Pareto Index Using the Greenwood Statistic
author Arendarczyk , Marek
author_facet Arendarczyk , Marek
J. Kozubowski , Tomasz
K. Panorska , Anna
author_role author
author2 J. Kozubowski , Tomasz
K. Panorska , Anna
author2_role author
author
dc.contributor.author.fl_str_mv Arendarczyk , Marek
J. Kozubowski , Tomasz
K. Panorska , Anna
dc.subject.por.fl_str_mv coefficient of variation
extremes
generalized Pareto distribution
heavy tailed distribution
power law
Peak-over-threshold
topic coefficient of variation
extremes
generalized Pareto distribution
heavy tailed distribution
power law
Peak-over-threshold
description The generalized Pareto distributions (GPDs) play an important role in the statistics of extremes. We point various problems with the likelihood-based inference for the index parameter α of the GPDs, and develop alternative testing strategies, which do not require parameter estimation. Our test statistic is the Greenwood statistic, which probability distribution is stochastically increasing with respect to α within the GPDs. We compare the performance of our test to a test with maximum-to-sum ratio test statistic Rn. New results on the properties of the Rn are also presented, as well as recommendations for calculating the p-values and illustrative data examples.
publishDate 2023
dc.date.none.fl_str_mv 2023-07-31
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 https://doi.org/10.57805/revstat.v21i3.357
https://doi.org/10.57805/revstat.v21i3.357
url https://doi.org/10.57805/revstat.v21i3.357
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://revstat.ine.pt/index.php/REVSTAT/article/view/357
https://revstat.ine.pt/index.php/REVSTAT/article/view/357/651
https://revstat.ine.pt/index.php/REVSTAT/article/view/357/540
dc.rights.driver.fl_str_mv Copyright (c) 2022 REVSTAT-Statistical Journal
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2022 REVSTAT-Statistical Journal
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Statistics Portugal
publisher.none.fl_str_mv Statistics Portugal
dc.source.none.fl_str_mv REVSTAT-Statistical Journal; Vol. 21 No. 3 (2023): REVSTAT-Statistical Journal; 367–388
REVSTAT; Vol. 21 N.º 3 (2023): REVSTAT-Statistical Journal; 367–388
2183-0371
1645-6726
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
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