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
Descripción
Sumario: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.