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Minimax Estimation of the Mean Matrix of the Matrix Variate Normal Distribution under the Divergence Loss Function

Author

Listed:
  • Shokofeh Zinodiny

    (Amirkabir University of Technology - Iran)

  • Sadegh Rezaei

    (Amirkabir University of Technology - Iran)

  • Saralees Nadarajah

    (University of Manchester - UK)

Abstract

The problem of estimating the mean matrix of a matrix-variate normal distribution with a covariance matrix is considered under two loss functions. We construct a class of empirical Bayes estimators which are better than the maximum likelihood estimator under the first loss function and hence show that the maximum likelihood estimator is inadmissible. We find a general class of minimax estimators. Also we give a class of estimators that improve on the maximum likelihood estimator under the second loss function and hence show that the maximum likelihood estimator is inadmissible.

Suggested Citation

  • Shokofeh Zinodiny & Sadegh Rezaei & Saralees Nadarajah, 2017. "Minimax Estimation of the Mean Matrix of the Matrix Variate Normal Distribution under the Divergence Loss Function," Statistica, Department of Statistics, University of Bologna, vol. 77(4), pages 369-384.
    • Handle: RePEc:bot:rivsta:v:77:y:2017:i:4:p:369-384
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    Cited by:

    1. Gong, Aibo & Ke, Shaowei & Qiu, Yawen & Shen, Rui, 2022. "Robust pricing under strategic trading," Journal of Economic Theory, Elsevier, vol. 199(C).
    2. Karamikabir, Hamid & Afshari, Mahmoud, 2020. "Generalized Bayesian shrinkage and wavelet estimation of location parameter for spherical distribution under balance-type loss: Minimaxity and admissibility," Journal of Multivariate Analysis, Elsevier, vol. 177(C).

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