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Maximum likelihood estimation of Wishart mean matrices under Löwner order restrictions


  • Tsai, Ming-Tien


For Wishart density functions, there remains a long-time question unsolved. That is whether there exists the closed-form MLEs of mean matrices over the partially Löwner ordering sets. In this note, we provide an affirmative answer by demonstrating a unified procedure on exactly how the closed-form MLEs are obtained for the simple ordering case. Under the Kullback-Leibler loss function, a property of obtained MLEs is further studied. Some applications of the obtained closed-form MLEs, including the comparison between our ML estimates and Calvin and Dykstra's [Maximum likelihood estimation of a set of covariance matrices under Löwner order restrictions with applications to balanced multivariate variance components models, Ann. Statist. 19 (1991) 850-869.] which obtained by iterative algorithm, are also made.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:5:p:932-944

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    References listed on IDEAS

    1. Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
    2. M. S. Srivastava & Tatsuya Kubokawa, 1999. "Improved Nonnegative Estimation of Multivariate Components of Variance," CIRJE F-Series CIRJE-F-38, CIRJE, Faculty of Economics, University of Tokyo.
    3. 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.
    4. Loh, Wei-Liem, 1991. "Estimating covariance matrices II," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 163-174, February.
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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.


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