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ML Estimation of the MultivariatetDistribution and the EM Algorithm

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  • Liu, Chuanhai

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.

Suggested Citation

  • Liu, Chuanhai, 1997. "ML Estimation of the MultivariatetDistribution and the EM Algorithm," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 296-312, November.
    • Handle: RePEc:eee:jmvana:v:63:y:1997:i:2:p:296-312
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    References listed on IDEAS

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    1. Roderick J. A. Little, 1988. "Robust Estimation of the Mean and Covariance Matrix from Data with Missing Values," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(1), pages 23-38, March.
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    Cited by:

    1. Uchenna Chinedu Nduka, 2022. "Efficient and robust estimation for autoregressive regression models using shape mixtures of skewt normal distribution," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1519-1551, September.
    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. 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.
    4. 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.
    5. Ke-Hai Yuan & Wai Chan & Yubin Tian, 2016. "Expectation-robust algorithm and estimating equations for means and dispersion matrix with missing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 329-351, April.
    6. Wang, Xiao, 2010. "Wiener processes with random effects for degradation data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 340-351, February.
    7. Ke-Hai Yuan & Zhiyong Zhang, 2012. "Robust Structural Equation Modeling with Missing Data and Auxiliary Variables," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 803-826, October.
    8. Tian, Guo-Liang & Ng, Kai Wang & Tan, Ming, 2008. "EM-type algorithms for computing restricted MLEs in multivariate normal distributions and multivariate t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4768-4778, June.
    9. 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.

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