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Maximum likelihood estimation of covariance matrices under simple tree ordering

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  • Tsai, Ming-Tien

Abstract

The closed-form maximum likelihood estimators for the completely balanced multivariate one-way random effect model are obtained by Anderson et al. (Ann. Statist. 14 (1986) 405). It remains open whether there exist the closed-form maximum likelihood estimators for the more general completely balanced multivariate multi-way random effects models. In this paper, a new parameterization technique for covariance matrices is used to grasp the inside structure of likelihood function so that the maximum likelihood equations can be dramatically simplified. As such we obtain the closed-form maximum likelihood estimators of covariance matrices for Wishart density functions over the simple tree ordering set, which can then be applied to get the maximum likelihood estimators for the completely balanced multivariate multi-way random effects models without interactions.

Suggested Citation

  • Tsai, Ming-Tien, 2004. "Maximum likelihood estimation of covariance matrices under simple tree ordering," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 292-303, May.
    • Handle: RePEc:eee:jmvana:v:89:y:2004:i:2:p:292-303
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    References listed on IDEAS

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    1. Rao, C. Radhakrishna, 1971. "Estimation of variance and covariance components--MINQUE theory," Journal of Multivariate Analysis, Elsevier, vol. 1(3), pages 257-275, September.
    2. Anderson, T. W., 1989. "The asymptotic distribution of the likelihood ratio criterion for testing rank in multivariate components of variance," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 72-79, July.
    3. Rao, C. Radhakrishna, 1971. "Minimum variance quadratic unbiased estimation of variance components," Journal of Multivariate Analysis, Elsevier, vol. 1(4), pages 445-456, December.
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    Cited by:

    1. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2011. "Modifying estimators of ordered positive parameters under the Stein loss," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 164-181, January.
    2. Tsai, Ming-Tien & Kubokawa, Tatsuya, 2007. "Estimation of Wishart mean matrices under simple tree ordering," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 945-959, May.
    3. Tsai, Ming-Tien, 2007. "Maximum likelihood estimation of Wishart mean matrices under Löwner order restrictions," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 932-944, May.

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