IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/99cf52.html
   My bibliography  Save this paper

"Estimating the Covariance Matrix: A New Approach", June 1999

Author

Listed:
  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

  • M. S. Srivastava

    (University of Toronto)

Abstract

In this paper, we consider the problem of estimating the covaraince matrix and the generalized variance when the observations follow a nonsingular multivariate normal distribution with unknown mean. A new method is presented to obtain a truncated estimator that utilizes the information available in the sample mean matrix and dominates the James-Stein minimax estimator. Several scale equivariant minimax estimators are also given. This method is then applied to obtain new truncated and improved estimators of the generalized variance; it also provides a new proof to the results of Shorrock and Zidek (1976) and Sinha (1976).

Suggested Citation

  • Tatsuya Kubokawa & M. S. Srivastava, 1999. ""Estimating the Covariance Matrix: A New Approach", June 1999," CIRJE F-Series CIRJE-F-52, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:99cf52
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/99/1999cf52.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sheena, Yo & Takemura, Akimichi, 1992. "Inadmissibility of non-order-preserving orthogonally invariant estimators of the covariance matrix in the case of Stein's loss," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 117-131, April.
    2. Sinha, Bimal Kumar, 1976. "On improved estimators of the generalized variance," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 617-625, December.
    3. M. S. Srivastava & Tatsuya Kubokawa, 1999. "Improved Nonnegative Estimation of Multivariate Components of Variance," CIRJE F-Series CIRJE-F-38, CIRJE, Faculty of Economics, University of Tokyo.
    4. Sarkar, Sanat K., 1989. "On improving the shortest length confidence interval for the generalized variance," Journal of Multivariate Analysis, Elsevier, vol. 31(1), pages 136-147, October.
    5. Perron, F., 1992. "Minimax estimators of a covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 43(1), pages 16-28, October.
    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. Kubokawa, T. & Srivastava, M. S., 2003. "Estimating the covariance matrix: a new approach," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 28-47, July.
    2. Tatsuya Kubokawa & M. S. Srivastava, 2002. "Estimating the Covariance Matrix: A New Approach," CIRJE F-Series CIRJE-F-162, CIRJE, Faculty of Economics, University of Tokyo.

    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. Kubokawa, T. & Srivastava, M. S., 2003. "Estimating the covariance matrix: a new approach," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 28-47, July.
    2. Tatsuya Kubokawa & M. S. Srivastava, 2002. "Estimating the Covariance Matrix: A New Approach," CIRJE F-Series CIRJE-F-162, CIRJE, Faculty of Economics, University of Tokyo.
    3. Sanat Sarkar, 1991. "Stein-type improvements of confidence intervals for the generalized variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 369-375, June.
    4. Tsukuma, Hisayuki, 2016. "Estimation of a high-dimensional covariance matrix with the Stein loss," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 1-17.
    5. Tsai, Ming-Tien & Kubokawa, Tatsuya, 2007. "Estimation of Wishart mean matrices under simple tree ordering," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 945-959, May.
    6. Konno, Yoshihiko, 2001. "Inadmissibility of the Maximum Likekihood Estimator of Normal Covariance Matrices with the Lattice Conditional Independence," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 33-51, October.
    7. Iliopoulos, George, 2008. "UMVU estimation of the ratio of powers of normal generalized variances under correlation," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1051-1069, July.
    8. Iliopoulos, George & Kourouklis, Stavros, 1999. "Improving on the Best Affine Equivariant Estimator of the Ratio of Generalized Variances," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 176-192, February.
    9. Hara, Hisayuki, 2001. "Other Classes of Minimax Estimators of Variance Covariance Matrix in Multivariate Normal Distribution," Journal of Multivariate Analysis, Elsevier, vol. 77(2), pages 175-186, May.
    10. Konno, Yoshihiko, 2007. "Estimation of normal covariance matrices parametrized by irreducible symmetric cones under Stein's loss," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 295-316, February.
    11. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2011. "Modifying estimators of ordered positive parameters under the Stein loss," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 164-181, January.
    12. Besson, Olivier & Vincent, François & Gendre, Xavier, 2020. "A Stein’s approach to covariance matrix estimation using regularization of Cholesky factor and log-Cholesky metric," Statistics & Probability Letters, Elsevier, vol. 167(C).
    13. Perron, François, 1997. "On a Conjecture of Krishnamoorthy and Gupta, ," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 110-120, July.
    14. Ali Jafari, 2012. "Inferences on the ratio of two generalized variances: independent and correlated cases," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 297-314, August.
    15. Ye, Ren-Dao & Wang, Song-Gui, 2009. "Improved estimation of the covariance matrix under Stein's loss," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 715-721, March.
    16. Takemura, Akimichi & Sheena, Yo, 2005. "Distribution of eigenvalues and eigenvectors of Wishart matrix when the population eigenvalues are infinitely dispersed and its application to minimax estimation of covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 94(2), pages 271-299, June.
    17. Tsai, Ming-Tien, 2007. "Maximum likelihood estimation of Wishart mean matrices under Löwner order restrictions," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 932-944, May.
    18. Kubokawa, Tatsuya & Tsai, Ming-Tien, 2006. "Estimation of covariance matrices in fixed and mixed effects linear models," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2242-2261, November.
    19. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    20. Tsukuma, Hisayuki & Konno, Yoshihiko, 2006. "On improved estimation of normal precision matrix and discriminant coefficients," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1477-1500, August.

    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:99cf52. 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.