Consistency of Maximum Likelihood Estimators in Finite Mixture Models of the Union of the Union of W-Type Families

In finite mixture models, maximum likelihood estimators have good properties, such as efficiency, consistency, and asymptotic normality under some uniform integrability assumptions on the mixture and its derivatives up to the third order. These conditions are frequently not easy to check because compl...

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Detalles Bibliográficos
Autores: Atienza Martínez, María Nieves, García Heras, Joaquín, Muñoz Pichardo, Juan Manuel
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2005
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/114824
Acceso en línea:https://hdl.handle.net/11441/114824
https://doi.org/10.1081/STA-200063297
Access Level:acceso abierto
Palabra clave:Consistency
Exponential families
Generalized Gamma
Mixtures
Weibull
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spelling Consistency of Maximum Likelihood Estimators in Finite Mixture Models of the Union of the Union of W-Type FamiliesAtienza Martínez, María NievesGarcía Heras, JoaquínMuñoz Pichardo, Juan ManuelConsistencyExponential familiesGeneralized GammaMixturesWeibullIn finite mixture models, maximum likelihood estimators have good properties, such as efficiency, consistency, and asymptotic normality under some uniform integrability assumptions on the mixture and its derivatives up to the third order. These conditions are frequently not easy to check because complex computations on bounding a lot of derivatives are involved. We give results implying these conditions for a new class of families of distributions, W-type families, which make it easier to check the conditions in many cases. Many useful and known families of distributions such as Weibull, Generalized Gamma, Log-gamma, inverse Log-gamma, inverse Gaussian, and all of the exponential families are W-type families. Hence, these results have broad applications.Dirección General de Enseñanza Superior BFM2001-3844Taylor and FrancisMatemática Aplicada IDirección General de Enseñanza Superior (DGES). España2005info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/114824https://doi.org/10.1081/STA-200063297reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésCommunications in Statistics: Theory and Methods, 34 (7), 1471-1485.BFM2001-3844https://www.tandfonline.com/doi/full/10.1081/STA-200063297info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1148242026-06-17T12:51:07Z
dc.title.none.fl_str_mv Consistency of Maximum Likelihood Estimators in Finite Mixture Models of the Union of the Union of W-Type Families
title Consistency of Maximum Likelihood Estimators in Finite Mixture Models of the Union of the Union of W-Type Families
spellingShingle Consistency of Maximum Likelihood Estimators in Finite Mixture Models of the Union of the Union of W-Type Families
Atienza Martínez, María Nieves
Consistency
Exponential families
Generalized Gamma
Mixtures
Weibull
title_short Consistency of Maximum Likelihood Estimators in Finite Mixture Models of the Union of the Union of W-Type Families
title_full Consistency of Maximum Likelihood Estimators in Finite Mixture Models of the Union of the Union of W-Type Families
title_fullStr Consistency of Maximum Likelihood Estimators in Finite Mixture Models of the Union of the Union of W-Type Families
title_full_unstemmed Consistency of Maximum Likelihood Estimators in Finite Mixture Models of the Union of the Union of W-Type Families
title_sort Consistency of Maximum Likelihood Estimators in Finite Mixture Models of the Union of the Union of W-Type Families
dc.creator.none.fl_str_mv Atienza Martínez, María Nieves
García Heras, Joaquín
Muñoz Pichardo, Juan Manuel
author Atienza Martínez, María Nieves
author_facet Atienza Martínez, María Nieves
García Heras, Joaquín
Muñoz Pichardo, Juan Manuel
author_role author
author2 García Heras, Joaquín
Muñoz Pichardo, Juan Manuel
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Dirección General de Enseñanza Superior (DGES). España
dc.subject.none.fl_str_mv Consistency
Exponential families
Generalized Gamma
Mixtures
Weibull
topic Consistency
Exponential families
Generalized Gamma
Mixtures
Weibull
description In finite mixture models, maximum likelihood estimators have good properties, such as efficiency, consistency, and asymptotic normality under some uniform integrability assumptions on the mixture and its derivatives up to the third order. These conditions are frequently not easy to check because complex computations on bounding a lot of derivatives are involved. We give results implying these conditions for a new class of families of distributions, W-type families, which make it easier to check the conditions in many cases. Many useful and known families of distributions such as Weibull, Generalized Gamma, Log-gamma, inverse Log-gamma, inverse Gaussian, and all of the exponential families are W-type families. Hence, these results have broad applications.
publishDate 2005
dc.date.none.fl_str_mv 2005
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/114824
https://doi.org/10.1081/STA-200063297
url https://hdl.handle.net/11441/114824
https://doi.org/10.1081/STA-200063297
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Communications in Statistics: Theory and Methods, 34 (7), 1471-1485.
BFM2001-3844
https://www.tandfonline.com/doi/full/10.1081/STA-200063297
dc.rights.none.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 Taylor and Francis
publisher.none.fl_str_mv Taylor and Francis
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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