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Penalized Maximum Likelihood Estimator for Normal Mixtures
Author(s) -
CIUPERCA GABRIELA,
RIDOLFI ANDREA,
IDIER JÉRÔME
Publication year - 2003
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00317
Subject(s) - mathematics , likelihood function , restricted maximum likelihood , estimator , likelihood principle , maximum likelihood sequence estimation , consistency (knowledge bases) , expectation–maximization algorithm , statistics , m estimator , maximum likelihood , marginal likelihood , bounded function , maximum a posteriori estimation , likelihood ratio test , function (biology) , quasi maximum likelihood , mathematical analysis , discrete mathematics , evolutionary biology , biology
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.