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Bayes minimax estimation of the multivariate normal mean vector under quadratic loss functions

Author

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  • Zinodiny, S.
  • Rezaei, S.
  • Arjmand, O. Naghshineh
  • Nadarajah, S.

Abstract

The problem of estimating the mean vector μ of a multivariate normal distribution with the covariance matrix σ2Ip is considered under the loss function, (δ−μ)′D(δ−μ)σ2, where σ2 is unknown and D is a known positive definite diagonal matrix. A large class of Bayes minimax estimators of μ is found. This class includes classes of estimators obtained by Lin and Mousa (1982) and Zinodiny et al. (2011).

Suggested Citation

  • Zinodiny, S. & Rezaei, S. & Arjmand, O. Naghshineh & Nadarajah, S., 2013. "Bayes minimax estimation of the multivariate normal mean vector under quadratic loss functions," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2052-2056.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:9:p:2052-2056
    DOI: 10.1016/j.spl.2013.05.021
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    References listed on IDEAS

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    1. Wells, Martin T. & Zhou, Gongfu, 2008. "Generalized Bayes minimax estimators of the mean of multivariate normal distribution with unknown variance," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2208-2220, November.
    2. Zinodiny, S. & Strawderman, W.E. & Parsian, A., 2011. "Bayes minimax estimation of the multivariate normal mean vector for the case of common unknown variance," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1256-1262, October.
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    Cited by:

    1. Zinodiny, S. & Rezaei, S. & Nadarajah, S., 2014. "Bayes minimax estimation of the multivariate normal mean vector under balanced loss function," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 96-101.
    2. Imai, Ryo & Kubokawa, Tatsuya & Ghosh, Malay, 2019. "Bayesian simultaneous estimation for means in k-sample problems," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 49-60.

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