Penalized Maximum Likelihood Estimator for Normal Mixtures |
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Authors: | GABRIELA CIUPERCA,REA RIDOLFI,& JÉ RÔ ME IDIER |
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Affiliation: | UniversitéLyon 1,;CNRS-Laboratoire des Signaux et Systèmes and École Polytechnique Fédérale de Lausanne,;CNRS-Laboratoire des Signaux et Systèmes |
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Abstract: | The estimation of the parameters of a mixture of Gaussian densities is considered, within the framework of maximum likelihood. Due to unboundedness of the likelihood function, the maximum likelihood estimator fails to exist. We adopt a solution to likelihood function degeneracy which consists in penalizing the likelihood function. The resulting penalized likelihood function is then bounded over the parameter space and the existence of the penalized maximum likelihood estimator is granted. As original contribution we provide asymptotic properties, and in particular a consistency proof, for the penalized maximum likelihood estimator. Numerical examples are provided in the finite data case, showing the performances of the penalized estimator compared to the standard one. |
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Keywords: | Bayesian estimation mixtures of normal distributions penalized maximum likelihood strong consistency |
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