Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with Applications
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | , , , |
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.v21i4.431 |
Resumo: | In this paper we study some methods to reduce the bias for maximum likelihood estimation in the general class of alpha power models, specifically for the shape parameter. We find the modified maximum likelihood estimator using Firth's method and we show that this estimator is the uniformly minimum variance unbiased estimator (UMVUE) in this class. We consider three special cases of this class, namely the exponentiated exponential (EE), the power half-normal and the power piecewise exponential models. We compare the bias in simulation studies and find that the modified method is definitely superior, especially for small sample sizes, in both the bias and the root mean squared error. We illustrate our modified estimator in four real data set examples, in each of which the modified estimates better explain the variability. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
spelling |
Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with ApplicationsUMVUEFirth's methodexponentiated exponential modelpower half-normal modelIn this paper we study some methods to reduce the bias for maximum likelihood estimation in the general class of alpha power models, specifically for the shape parameter. We find the modified maximum likelihood estimator using Firth's method and we show that this estimator is the uniformly minimum variance unbiased estimator (UMVUE) in this class. We consider three special cases of this class, namely the exponentiated exponential (EE), the power half-normal and the power piecewise exponential models. We compare the bias in simulation studies and find that the modified method is definitely superior, especially for small sample sizes, in both the bias and the root mean squared error. We illustrate our modified estimator in four real data set examples, in each of which the modified estimates better explain the variability.Statistics Portugal2023-11-09info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://doi.org/10.57805/revstat.v21i4.431https://doi.org/10.57805/revstat.v21i4.431REVSTAT-Statistical Journal; Vol. 21 No. 4 (2023): REVSTAT-Statistical Journal; 491–507REVSTAT; Vol. 21 N.º 4 (2023): REVSTAT-Statistical Journal; 491–5072183-03711645-6726reponame: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/431https://revstat.ine.pt/index.php/REVSTAT/article/view/431/664https://revstat.ine.pt/index.php/REVSTAT/article/view/431/665Gómez, Yolanda M.Santos, BrunoGallardo, Diego I.Venegas , OsvaldoGómez, Héctor W.info:eu-repo/semantics/openAccess2023-11-11T06:30:22Zoai:revstat:article/431Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:37:57.540046Repositório 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 |
Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with Applications |
title |
Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with Applications |
spellingShingle |
Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with Applications Gómez, Yolanda M. UMVUE Firth's method exponentiated exponential model power half-normal model |
title_short |
Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with Applications |
title_full |
Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with Applications |
title_fullStr |
Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with Applications |
title_full_unstemmed |
Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with Applications |
title_sort |
Bias Reduction of Maximum Likelihood Estimates for an Asymmetric Class of Power Models with Applications |
author |
Gómez, Yolanda M. |
author_facet |
Gómez, Yolanda M. Santos, Bruno Gallardo, Diego I. Venegas , Osvaldo Gómez, Héctor W. |
author_role |
author |
author2 |
Santos, Bruno Gallardo, Diego I. Venegas , Osvaldo Gómez, Héctor W. |
author2_role |
author author author author |
dc.contributor.author.fl_str_mv |
Gómez, Yolanda M. Santos, Bruno Gallardo, Diego I. Venegas , Osvaldo Gómez, Héctor W. |
dc.subject.por.fl_str_mv |
UMVUE Firth's method exponentiated exponential model power half-normal model |
topic |
UMVUE Firth's method exponentiated exponential model power half-normal model |
description |
In this paper we study some methods to reduce the bias for maximum likelihood estimation in the general class of alpha power models, specifically for the shape parameter. We find the modified maximum likelihood estimator using Firth's method and we show that this estimator is the uniformly minimum variance unbiased estimator (UMVUE) in this class. We consider three special cases of this class, namely the exponentiated exponential (EE), the power half-normal and the power piecewise exponential models. We compare the bias in simulation studies and find that the modified method is definitely superior, especially for small sample sizes, in both the bias and the root mean squared error. We illustrate our modified estimator in four real data set examples, in each of which the modified estimates better explain the variability. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-11-09 |
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.v21i4.431 https://doi.org/10.57805/revstat.v21i4.431 |
url |
https://doi.org/10.57805/revstat.v21i4.431 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://revstat.ine.pt/index.php/REVSTAT/article/view/431 https://revstat.ine.pt/index.php/REVSTAT/article/view/431/664 https://revstat.ine.pt/index.php/REVSTAT/article/view/431/665 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
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. 4 (2023): REVSTAT-Statistical Journal; 491–507 REVSTAT; Vol. 21 N.º 4 (2023): REVSTAT-Statistical Journal; 491–507 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 |
repository.mail.fl_str_mv |
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1799134938055835648 |