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...
| Autores: | , , , |
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| 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 |
| 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. |
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