IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2002cf187.html
   My bibliography  Save this paper

Minimax Multivariate Empirical Bayes Estimators under Multicollinearity

Author

Listed:
  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

  • M. S. Srivastava

    (Department of Statistics, University of Toronto)

Abstract

In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption of normality, we propose empirical Bayes ridge regression estimators with three types of shrinkage functions,that is, scalar, componentwise and matricial shrinkage. These proposed estimators are proved to be uniformly better than the least squares estimator, that is, minimax in terms of risk under the Strawderman's loss function. Through simulation and empirical studies, they are also shown to be useful in the multicollinearity cases.

Suggested Citation

  • 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.
  • Handle: RePEc:tky:fseres:2002cf187
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2002/2002cf187.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
    2. Bilodeau, Martin & Kariya, Takeaki, 1989. "Minimax estimators in the normal MANOVA model," Journal of Multivariate Analysis, Elsevier, vol. 28(2), pages 260-270, February.
    3. 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.
    4. 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.
    5. 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.
    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. Oman, Samuel D., 2002. "Minimax Hierarchical Empirical Bayes Estimation in Multivariate Regression," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 285-301, February.
    3. 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.
    4. 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.
    5. Xu, Kai & He, Daojiang, 2015. "Further results on estimation of covariance matrix," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 11-20.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Fourdrinier Dominique & Strawderman William E. & Wells Martin T., 2009. "Improved estimation for elliptically symmetric distributions with unknown block diagonal covariance matrix," Statistics & Risk Modeling, De Gruyter, vol. 26(3), pages 203-217, April.
    11. Mori, Yuichi & Suzuki, Taiji, 2018. "Generalized ridge estimator and model selection criteria in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 243-261.
    12. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2015. "A unified approach to estimating a normal mean matrix in high and low dimensions," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 312-328.
    13. 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.
    14. 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.
    15. Tsukuma, Hisayuki, 2010. "Shrinkage minimax estimation and positive-part rule for a mean matrix in an elliptically contoured distribution," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 215-220, February.
    16. 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.
    17. 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.
    18. Andrew F. Siegel & Artemiza Woodgate, 2007. "Performance of Portfolios Optimized with Estimation Error," Management Science, INFORMS, vol. 53(6), pages 1005-1015, June.
    19. Kubokawa, Tatsuya & Srivastava, Muni S., 2008. "Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1906-1928, October.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    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:tky:fseres:2002cf187. 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: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.html .

    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.