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Estimation of Several Wishart Mean Matrices

Author

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  • Ming-Tien Tsai

    (Institute of Statistical Science, Academia Sinica)

  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

Abstract

For Wishart density functions, the risk dominance problems of moment estimators, maximum likelihood estimators (MLEs), James-Stein type minimax estimators and their improved estimators of covariance matrices under the Kullback-Leibler loss function have been well studied in the literature. However, attentions have mostly paid on the onesample and the two-sample problems. In this paper, it emphasizes on two-folds for the k-sample problem: (i) based on the sample covariance matrices (moment estimators), by incorporating the Cholesky decomposition to establish the James-Stein type estimators both over the whole parameter space and over the restricted parameter space under the simple tree ordering set, respectively, (ii) based on the corresponding MLEs, by incorporating the spectrum decomposition and its new generalization to propose a unified procedure to construct the improved estimators both over the whole parameter space and over the restricted parameter space under the simple tree ordering set, respectively. The results are directly applied to the estimation of covariance matrices for the completely balanced multivariate multi-way random effects models without interactions.

Suggested Citation

  • Ming-Tien Tsai & Tatsuya Kubokawa, 2005. "Estimation of Several Wishart Mean Matrices," CIRJE F-Series CIRJE-F-349, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2005cf349
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    Cited by:

    1. 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.

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