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Maximum likelihood estimation of Wishart mean matrices under Löwner order restrictions


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  • Tsai, Ming-Tien
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    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.

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

    Volume (Year): 98 (2007)
    Issue (Month): 5 (May)
    Pages: 932-944

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

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    Keywords: Exterior differential forms Matrix factorizations Kullback-Leibler loss function Simple ordering set Wishart density function;


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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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