IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v82y2002i1p39-64.html
   My bibliography  Save this article

Estimating Risk and the Mean Squared Error Matrix in Stein Estimation

Author

Listed:
  • Kubokawa, T.
  • Srivastava, M. S.

Abstract

It is well known that the uniformly minimum variance unbiased (UMVU) estimators of the risk and the mean squared error (MSE) matrix proposed in the literature for Stein estimators can take negative values with positive probability. In this paper, improved truncated estimators of the risk, risk difference, and MSE matrix are proposed and shown to be better than the UMVU estimators in terms of mean squared error.

Suggested Citation

  • Kubokawa, T. & Srivastava, M. S., 2002. "Estimating Risk and the Mean Squared Error Matrix in Stein Estimation," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 39-64, July.
    • Handle: RePEc:eee:jmvana:v:82:y:2002:i:1:p:39-64
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(01)92020-2
    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. Carter, R.A.L. & Srivastava, M.S. & Srivastava, V.K. & Ullah, A., 1990. "Unbiased Estimation of the MSE Matrix of Stein-Rule Estimators, Confidence Ellipsoids, and Hypothesis Testing," Econometric Theory, Cambridge University Press, vol. 6(1), pages 63-74, March.
    2. Konno, Yoshihiko, 1991. "On estimation of a matrix of normal means with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 36(1), pages 44-55, January.
    3. Casella, George, 1990. "Estimators with nondecreasing risk: application of a chi-squared identity," Statistics & Probability Letters, Elsevier, vol. 10(2), pages 107-109, July.
    4. Kleffe, J. & Rao, J. N. K., 1992. "Estimation of mean square error of empirical best linear unbiased predictors under a random error variance linear model," Journal of Multivariate Analysis, Elsevier, vol. 43(1), pages 1-15, October.
    5. Bilodeau, Martin & Kariya, Takeaki, 1989. "Minimax estimators in the normal MANOVA model," Journal of Multivariate Analysis, Elsevier, vol. 28(2), pages 260-270, February.
    6. Leo Breiman & Jerome H. Friedman, 1997. "Predicting Multivariate Responses in Multiple Linear Regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 3-54.
    Full references (including those not matched with items on IDEAS)

    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. Srivastava, M. S. & Kubokawa, T., 2005. "Minimax multivariate empirical Bayes estimators under multicollinearity," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 394-416, April.
    2. Tatsuya Kubokawa & M. S. Srivastava, 2002. "Minimax Multivariate Empirical Bayes Estimators under Multicollinearity," CIRJE F-Series CIRJE-F-187, CIRJE, Faculty of Economics, University of Tokyo.
    3. Oman, Samuel D., 2002. "Minimax Hierarchical Empirical Bayes Estimation in Multivariate Regression," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 285-301, February.
    4. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2007. "Methods for improvement in estimation of a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1592-1610, September.
    5. Hisayuki Tsukuma & Tatsuya Kubokawa, 2005. "Methods for Improvement in Estimation of a Normal Mean Matrix," CIRJE F-Series CIRJE-F-378, CIRJE, Faculty of Economics, University of Tokyo.
    6. Hisayuki Tsukuma & Tatsuya Kubokawa, 2014. "A Unified Approach to Estimating a Normal Mean Matrix in High and Low Dimensions," CIRJE F-Series CIRJE-F-926, CIRJE, Faculty of Economics, University of Tokyo.
    7. Kubokawa, T. & Srivastava, M. S., 2001. "Robust Improvement in Estimation of a Mean Matrix in an Elliptically Contoured Distribution," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 138-152, January.
    8. Tsukuma, Hisayuki, 2009. "Generalized Bayes minimax estimation of the normal mean matrix with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2296-2304, November.
    9. Shokofeh Zinodiny & Saralees Nadarajah, 2024. "A New Class of Bayes Minimax Estimators of the Mean Matrix of a Matrix Variate Normal Distribution," Mathematics, MDPI, vol. 12(7), pages 1-14, April.
    10. Xu, Kai & He, Daojiang, 2015. "Further results on estimation of covariance matrix," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 11-20.
    11. Tatsuka Kubokawa & M. S. Srivastava, 2002. "Prediction in Multivariate Mixed Linear Models," CIRJE F-Series CIRJE-F-180, CIRJE, Faculty of Economics, University of Tokyo.
    12. Paul Hewson & Keming Yu, 2008. "Quantile regression for binary performance indicators," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(5), pages 401-418, September.
    13. Jewson Stephen & Penzer Jeremy, 2006. "Estimating Trends in Weather Series: Consequences for Pricing Derivatives," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-17, September.
    14. Luebke, Karsten & Czogiel, Irina & Weihs, Claus, 2004. "Latent Factor Prediction Pursuit for Rank Deficient Regressors," Technical Reports 2004,75, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    15. Seokhyun Chung & Raed Al Kontar & Zhenke Wu, 2022. "Weakly Supervised Multi-output Regression via Correlated Gaussian Processes," INFORMS Joural on Data Science, INFORMS, vol. 1(2), pages 115-137, October.
    16. Qiang Sun & Hongtu Zhu & Yufeng Liu & Joseph G. Ibrahim, 2015. "SPReM: Sparse Projection Regression Model For High-Dimensional Linear Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 289-302, March.
    17. Tsukuma, Hisayuki, 2010. "Shrinkage priors for Bayesian estimation of the mean matrix in an elliptically contoured distribution," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1483-1492, July.
    18. Simila, Timo & Tikka, Jarkko, 2007. "Input selection and shrinkage in multiresponse linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 406-422, September.
    19. Flandoli, F. & Giorgi, E. & Aspinall, W.P. & Neri, A., 2011. "Comparison of a new expert elicitation model with the Classical Model, equal weights and single experts, using a cross-validation technique," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1292-1310.
    20. Peter A. Gao & Jonathan Wakefield, 2023. "A Spatial Variance‐Smoothing Area Level Model for Small Area Estimation of Demographic Rates," International Statistical Review, International Statistical Institute, vol. 91(3), pages 493-510, December.

    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:82:y:2002:i:1:p:39-64. 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.