On the consistency of MLE in finite mixture models of exponential families
| Autor: | Nieves Atienza, J. M. Muñoz-Pichardo, Rafael Villa, J. García-Heras |
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| Rok vydání: | 2007 |
| Předmět: |
Statistics and Probability
Applied Mathematics Asymptotic distribution Density estimation Function (mathematics) Upper and lower bounds Exponential family Consistency (statistics) Statistics Expectation–maximization algorithm Applied mathematics Statistics Probability and Uncertainty Likelihood function Mathematics |
| Zdroj: | Journal of Statistical Planning and Inference. 137:496-505 |
| ISSN: | 0378-3758 |
| DOI: | 10.1016/j.jspi.2005.12.014 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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