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Inference for multivariate normal mixtures

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  • Chen, Jiahua
  • Tan, Xianming
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    Abstract

    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. In this paper, 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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 100 (2009)
    Issue (Month): 7 (August)
    Pages: 1367-1383

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    Handle: RePEc:eee:jmvana:v:100:y:2009:i:7:p:1367-1383

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    Keywords: Multivariate normal mixture Penalized maximum likelihood estimator Strong consistency;

    References

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    1. Raftery, Adrian E. & Dean, Nema, 2006. "Variable Selection for Model-Based Clustering," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 168-178, March.
    2. Tadesse, Mahlet G. & Sha, Naijun & Vannucci, Marina, 2005. "Bayesian Variable Selection in Clustering High-Dimensional Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 602-617, June.
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    Cited by:
    1. Ingrassia, Salvatore & Rocci, Roberto, 2011. "Degeneracy of the EM algorithm for the MLE of multivariate Gaussian mixtures and dynamic constraints," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1715-1725, April.
    2. Nicolas Depraetere & Martina Vandebroek, 2014. "Order selection in finite mixtures of linear regressions," Statistical Papers, Springer, vol. 55(3), pages 871-911, August.
    3. Kim, Daeyoung & Seo, Byungtae, 2014. "Assessment of the number of components in Gaussian mixture models in the presence of multiple local maximizers," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 100-120.
    4. Seo, Byungtae & Lindsay, Bruce G., 2010. "A computational strategy for doubly smoothed MLE exemplified in the normal mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1930-1941, August.

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