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ML Estimation of the MultivariatetDistribution and the EM Algorithm

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  • Liu, Chuanhai
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    Abstract

    Maximum likelihood estimation of the multivariatetdistribution, especially with unknown degrees of freedom, has been an interesting topic in the development of the EM algorithm. After a brief review of the EM algorithm and its application to finding the maximum likelihood estimates of the parameters of thetdistribution, this paper provides new versions of the ECME algorithm for maximum likelihood estimation of the multivariatetdistribution from data with possibly missing values. The results show that the new versions of the ECME algorithm converge faster than the previous procedures. Most important, the idea of this new implementation is quite general and useful for the development of the EM algorithm. Comparisons of different methods based on two datasets are presented.

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    Bibliographic Info

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

    Volume (Year): 63 (1997)
    Issue (Month): 2 (November)
    Pages: 296-312

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    Handle: RePEc:eee:jmvana:v:63:y:1997:i:2:p:296-312

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    Related research

    Keywords: EM ECM ECME incomplete data Newton-Raphson;

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    Cited by:
    1. Ke-Hai Yuan & Zhiyong Zhang, 2012. "Robust Structural Equation Modeling with Missing Data and Auxiliary Variables," Psychometrika, Springer, vol. 77(4), pages 803-826, October.
    2. Jie Jiang & Xinsheng Liu & Keming Yu, 2013. "Maximum likelihood estimation of multinomial probit factor analysis models for multivariate t-distribution," Computational Statistics, Springer, vol. 28(4), pages 1485-1500, August.
    3. Wang, Xiao, 2010. "Wiener processes with random effects for degradation data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 340-351, February.
    4. Chen, Tao & Martin, Elaine & Montague, Gary, 2009. "Robust probabilistic PCA with missing data and contribution analysis for outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3706-3716, August.
    5. Yuan, Ke-Hai, 2009. "Normal distribution based pseudo ML for missing data: With applications to mean and covariance structure analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1900-1918, October.
    6. Yuan, Ke-Hai & Savalei, Victoria, 2014. "Consistency, bias and efficiency of the normal-distribution-based MLE: The role of auxiliary variables," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 353-370.

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