Artículo
On the consistency of MLE in finite mixture models of exponential families
Autor/es | Atienza Martínez, María Nieves
García Heras, Joaquín Muñoz Pichardo, Juan Manuel Villa Caro, Rafael |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de Estadística e Investigación Operativa Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2007 |
Fecha de depósito | 2021-06-24 |
Publicado en |
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Resumen | 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 ... 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. |
Cita | Atienza Martínez, M.N., García Heras, J., Muñoz Pichardo, J.M. y Villa Caro, R. (2007). On the consistency of MLE in finite mixture models of exponential families. Journal of Statistical Planning and Inference, 137 (2), 496-505. |
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