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Analytic calculations for the EM algorithm for multivariate skew-t mixture models


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  • Vrbik, I.
  • McNicholas, P.D.
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    The em algorithm can be used to compute maximum likelihood estimates of model parameters for skew-t mixture models. We show that the intractable expectations needed in the e-step can be written out analytically. These closed form expressions bypass the need for numerical estimation procedures, such as Monte Carlo methods, leading to accurate calculation of maximum likelihood estimates. Our approach is illustrated on two real data sets.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 6 ()
    Pages: 1169-1174

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:6:p:1169-1174

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    Keywords: Multivariate skew-t distribution; Mixture models; em algorithm; Skewness;


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    1. Hua Zhou & Kenneth L. Lange, 2010. "On the Bumpy Road to the Dominant Mode," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 37(4), pages 612-631.
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    Cited by:
    1. Vrbik, Irene & McNicholas, Paul D., 2014. "Parsimonious skew mixture models for model-based clustering and classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 196-210.
    2. Sanjeena Subedi & Paul McNicholas, 2014. "Variational Bayes approximations for clustering via mixtures of normal inverse Gaussian distributions," Advances in Data Analysis and Classification, Springer, vol. 8(2), pages 167-193, June.
    3. Bouveyron, Charles & Brunet-Saumard, Camille, 2014. "Model-based clustering of high-dimensional data: A review," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 52-78.


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