IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v96y2005i1p55-72.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(04)00176-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ahmed, S. Ejaz & Nicol, Christopher J., 2012. "An application of shrinkage estimation to the nonlinear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3309-3321.
    2. T. Kubokawa & C. Robert & A. Saleh, 1991. "Robust estimation of common regression coefficients under spherical symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(4), pages 677-688, December.
    3. Wei, Laisheng & Chen, Jiahua, 2003. "Empirical Bayes estimation and its superiority for two-way classification model," Statistics & Probability Letters, Elsevier, vol. 63(2), pages 165-175, June.
    4. Zhang, Weiping & Wei, Laisheng & Yang, Yaning, 2005. "The superiority of empirical Bayes estimator of parameters in linear model," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 43-50, April.
    5. G. Trenkler & L. Wei, 1996. "The Bayes estimator in a misspecified linear regression model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 5(1), pages 113-123, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:96:y:2005:i:1:p:55-72. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.