## Inference for multivariate normal mixtures.(English)Zbl 1162.62052

Summary: Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical likelihood-based methods, which may have nice practical properties, are inconsistent. We recommend a penalized likelihood method for estimating the mixing distribution. We show that the maximum penalized likelihood estimator is strongly consistent when the number of components has a known upper bound. We also explore a convenient EM-algorithm for computing the maximum penalized likelihood estimator. Extensive simulations are conducted to explore the effectiveness and the practical limitations of both the new method and the ratified maximum likelihood estimators. Guidelines are provided based on the simulation results.

### MSC:

 62H12 Estimation in multivariate analysis 62F12 Asymptotic properties of parametric estimators 65C60 Computational problems in statistics (MSC2010) 62F10 Point estimation
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### References:

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