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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Detalles Bibliográficos
Autores: Atienza Martínez, María Nieves, García Heras, Joaquín, Muñoz Pichardo, Juan Manuel, Villa Caro, Rafael
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2007
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/114802
Acceso en línea:https://hdl.handle.net/11441/114802
https://doi.org/10.1016/j.jspi.2005.12.014
Access Level:acceso abierto
Palabra clave:Consistency
Exponential families
Mixtures
Descripción
Sumario: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.