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Estimation of the mean vector of a multivariate normal distribution: subspace hypothesis

Author

Listed:
  • Srivastava, M.S.
  • Ehsanes Saleh, A.K.Md.

Abstract

This paper considers the estimation of the mean vector [theta] of a p-variate normal distribution with unknown covariance matrix [Sigma] when it is suspected that for a pxr known matrix B the hypothesis [theta]=B[eta], may hold. We consider empirical Bayes estimators which includes (i) the unrestricted unbiased (UE) estimator, namely, the sample mean vector (ii) the restricted estimator (RE) which is obtained when the hypothesis [theta]=B[eta] holds (iii) the preliminary test estimator (PTE), (iv) the James-Stein estimator (JSE), and (v) the positive-rule Stein estimator (PRSE). The biases and the risks under the squared loss function are evaluated for all the five estimators and compared. The numerical computations show that PRSE is the best among all the five estimators even when the hypothesis [theta]=B[eta] is true.

Suggested Citation

  • Srivastava, M.S. & Ehsanes Saleh, A.K.Md., 2005. "Estimation of the mean vector of a multivariate normal distribution: subspace hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 55-72, September.
    • Handle: RePEc:eee:jmvana:v:96:y:2005:i:1:p:55-72
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    References listed on IDEAS

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    1. Ghosh M. & Saleh A.K.Md.E. & Sen P.K., 1989. "Empirical Bayes Subset Estimation In Regression Models," Statistics & Risk Modeling, De Gruyter, vol. 7(1-2), pages 15-36, February.
    2. Bilodeau, M., 1995. "Minimax Estimators of the Mean Vector in Normal Mixed Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 73-82, January.
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    Cited by:

    1. Tiefeng Ma & Shuangzhe Liu, 2013. "Estimation of order-restricted means of two normal populations under the LINEX loss function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 409-425, April.
    2. M. Arashi & S. Tabatabaey, 2010. "Estimation of the location parameter under LINEX loss function: multivariate case," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 51-57, July.
    3. 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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