On the consistency of MLE in finite mixture models of exponential families.(English)Zbl 1102.62020

Summary: 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 provides 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. R. A. Redner and H. F. Walker [Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev. 26, 195–239 (1984; Zbl 0536.62021)] 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.

MSC:

 62F12 Asymptotic properties of parametric estimators 62E10 Characterization and structure theory of statistical distributions

Zbl 0536.62021
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