IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v88y2004i1p131-137.html
   My bibliography  Save this article

Improved estimation of a covariance matrix in an elliptically contoured matrix distribution

Author

Listed:
  • Leung, Pui Lam
  • Ng, Foon Yip

Abstract

In this paper, the problem of estimating the covariance matrix of the elliptically contoured distribution (ECD) is considered. A new class of estimators which shrink the eigenvalues towards their arithmetic mean is proposed. It is shown that this new estimator dominates the unbiased estimator under the squared error loss function. Two special classes of ECD, namely, the multivariate-elliptical t distribution and the [var epsilon]-contaminated normal distribution are considered. A simulation study is carried out and indicates that this new shrinkage estimator provides a substantial improvement in risk under most situations.

Suggested Citation

  • Leung, Pui Lam & Ng, Foon Yip, 2004. "Improved estimation of a covariance matrix in an elliptically contoured matrix distribution," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 131-137, January.
    • Handle: RePEc:eee:jmvana:v:88:y:2004:i:1:p:131-137
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(03)00063-0
    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. 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. Pui Leung & Wai Chan, 1998. "Estimation of the Scale Matrix and its Eigenvalues in the Wishart and the Multivariate F Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 523-530, September.
    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. Fourdrinier, Dominique & Mezoued, Fatiha & Wells, Martin T., 2016. "Estimation of the inverse scatter matrix of an elliptically symmetric distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 32-55.
    2. 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.
    3. Besson, Olivier & Abramovich, Yuri I., 2014. "Invariance properties of the likelihood ratio for covariance matrix estimation in some complex elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 237-246.

    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. Andrew F. Siegel & Artemiza Woodgate, 2007. "Performance of Portfolios Optimized with Estimation Error," Management Science, INFORMS, vol. 53(6), pages 1005-1015, June.
    2. 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.
    3. K. Krishnamoorthy, 1991. "Estimation of a common multivariate normal mean vector," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(4), pages 761-771, December.
    4. Francesco Lautizi, 2015. "Large Scale Covariance Estimates for Portfolio Selection," CEIS Research Paper 353, Tor Vergata University, CEIS, revised 07 Aug 2015.
    5. Konno, Yoshihiko, 2009. "Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2237-2253, November.
    6. Tsukada, Shin-ichi, 2014. "Asymptotic expansion for distribution of the trace of a covariance matrix under a two-step monotone incomplete sample," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 206-219.
    7. Elfessi, Abdulaziz & Chun Jin, 1996. "On robust estimation of the common scale parameter of several Pareto distributions," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 345-352, September.
    8. 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.
    9. 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.
    10. Chang, Ching-Hui & Pal, Nabendu, 2008. "Testing on the common mean of several normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 321-333, December.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    16. 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.
    17. David Stefanovits & Urs Schubiger & Mario V. Wüthrich, 2014. "Model Risk in Portfolio Optimization," Risks, MDPI, vol. 2(3), pages 1-34, August.
    18. Kubokawa, Tatsuya & Hyodo, Masashi & Srivastava, Muni S., 2013. "Asymptotic expansion and estimation of EPMC for linear classification rules in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 496-515.
    19. Chételat, Didier & Wells, Martin T., 2016. "Improved second order estimation in the singular multivariate normal model," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 1-19.
    20. 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.

    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:88:y:2004:i:1:p:131-137. 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.