On the consistency of MLE in finite mixture models of exponential families

Finite mixtures of densities from an exponential family are frequently used in the statistical analysis of data. Modelling by finite mixtures of densities from different exponential families provide more flexibility in the fittings, and get better results. However, in mixture problems, the log-likel...

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Detalhes bibliográficos
Autores: Atienza Martínez, María Nieves, García Heras, Joaquín, Muñoz Pichardo, Juan Manuel, Villa Caro, Rafael
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2007
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/114802
Acesso em linha:https://hdl.handle.net/11441/114802
https://doi.org/10.1016/j.jspi.2005.12.014
Access Level:acceso abierto
Palavra-chave:Consistency
Exponential families
Mixtures
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spelling On the consistency of MLE in finite mixture models of exponential familiesAtienza Martínez, María NievesGarcía Heras, JoaquínMuñoz Pichardo, Juan ManuelVilla Caro, RafaelConsistencyExponential familiesMixturesFinite mixtures of densities from an exponential family are frequently used in the statistical analysis of data. Modelling by finite mixtures of densities from different exponential families provide more flexibility in the fittings, and get better results. However, in mixture problems, the log-likelihood function very often does not have an upper bound and therefore a global maximum does not always exist. Redner and Walker (1984. Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev. 26, 195–239) provide conditions to assure the existence, consistency and asymptotic normality of the maximum likelihood estimator. These conditions are not generally easy to check, even for mixtures of densities from exponential families and, especially, from different exponential families. In this paper, results are given which make verification of the conditions easier in both cases.ElsevierMatemática Aplicada IEstadística e Investigación OperativaAnálisis Matemático2007info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/114802https://doi.org/10.1016/j.jspi.2005.12.014reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Statistical Planning and Inference, 137 (2), 496-505.https://www.sciencedirect.com/science/article/pii/S0378375806000425info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1148022026-06-17T12:51:07Z
dc.title.none.fl_str_mv On the consistency of MLE in finite mixture models of exponential families
title On the consistency of MLE in finite mixture models of exponential families
spellingShingle On the consistency of MLE in finite mixture models of exponential families
Atienza Martínez, María Nieves
Consistency
Exponential families
Mixtures
title_short On the consistency of MLE in finite mixture models of exponential families
title_full On the consistency of MLE in finite mixture models of exponential families
title_fullStr On the consistency of MLE in finite mixture models of exponential families
title_full_unstemmed On the consistency of MLE in finite mixture models of exponential families
title_sort On the consistency of MLE in finite mixture models of exponential families
dc.creator.none.fl_str_mv Atienza Martínez, María Nieves
García Heras, Joaquín
Muñoz Pichardo, Juan Manuel
Villa Caro, Rafael
author Atienza Martínez, María Nieves
author_facet Atienza Martínez, María Nieves
García Heras, Joaquín
Muñoz Pichardo, Juan Manuel
Villa Caro, Rafael
author_role author
author2 García Heras, Joaquín
Muñoz Pichardo, Juan Manuel
Villa Caro, Rafael
author2_role author
author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Estadística e Investigación Operativa
Análisis Matemático
dc.subject.none.fl_str_mv Consistency
Exponential families
Mixtures
topic Consistency
Exponential families
Mixtures
description Finite mixtures of densities from an exponential family are frequently used in the statistical analysis of data. Modelling by finite mixtures of densities from different exponential families provide more flexibility in the fittings, and get better results. However, in mixture problems, the log-likelihood function very often does not have an upper bound and therefore a global maximum does not always exist. Redner and Walker (1984. Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev. 26, 195–239) provide conditions to assure the existence, consistency and asymptotic normality of the maximum likelihood estimator. These conditions are not generally easy to check, even for mixtures of densities from exponential families and, especially, from different exponential families. In this paper, results are given which make verification of the conditions easier in both cases.
publishDate 2007
dc.date.none.fl_str_mv 2007
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/11441/114802
https://doi.org/10.1016/j.jspi.2005.12.014
url https://hdl.handle.net/11441/114802
https://doi.org/10.1016/j.jspi.2005.12.014
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Statistical Planning and Inference, 137 (2), 496-505.
https://www.sciencedirect.com/science/article/pii/S0378375806000425
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 Elsevier
publisher.none.fl_str_mv Elsevier
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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