IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i4p742-752.html
   My bibliography  Save this article

Estimation of the precision matrix of multivariate Kotz type model

Author

Listed:
  • Sarr, Amadou
  • Gupta, Arjun K.

Abstract

In this paper, the problem of estimating the precision matrix of a multivariate Kotz type model is considered. First, using the quadratic loss function, we prove that the unbiased estimator , where denotes the sample sum of product matrix, is dominated by a better constant multiple of , denoted by . Secondly, a new class of shrinkage estimators of is proposed. Moreover, the risk functions of , and the proposed estimators are explicitly derived. It is shown that the proposed estimator dominates , under the quadratic loss function. A simulation study is carried out which confirms these results. Improved estimator of is also obtained.

Suggested Citation

  • Sarr, Amadou & Gupta, Arjun K., 2009. "Estimation of the precision matrix of multivariate Kotz type model," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 742-752, April.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:4:p:742-752
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(08)00180-2
    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. 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. J. K. Lindsey, 1999. "Multivariate Elliptically Contoured Distributions for Repeated Measurements," Biometrics, The International Biometric Society, vol. 55(4), pages 1277-1280, December.
    3. Kano, Y., 1994. "Consistency Property of Elliptic Probability Density Functions," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 139-147, October.
    4. Dipak Dey, 1988. "Simultaneous estimation of eigenvalues," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(1), pages 137-147, March.
    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. Taras Bodnar & Arjun K. Gupta & Nestor Parolya, 2013. "Optimal Linear Shrinkage Estimator for Large Dimensional Precision Matrix," Papers 1308.0931, arXiv.org, revised Mar 2014.
    2. Bodnar, Taras & Gupta, Arjun K. & Parolya, Nestor, 2016. "Direct shrinkage estimation of large dimensional precision matrix," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 223-236.
    3. Hashorva, Enkelejd, 2010. "On the residual dependence index of elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1070-1078, July.
    4. Taras Bodnar & Arjun Gupta, 2013. "An exact test for a column of the covariance matrix based on a single observation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 847-855, August.

    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. Li, Run-Ze & Fang, Kai-Tai, 1995. "Estimation of scale matrix of elliptically contoured matrix distributions," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 289-297, September.
    2. Andrew F. Siegel & Artemiza Woodgate, 2007. "Performance of Portfolios Optimized with Estimation Error," Management Science, INFORMS, vol. 53(6), pages 1005-1015, June.
    3. 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.
    4. 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.
    5. Francesco Lautizi, 2015. "Large Scale Covariance Estimates for Portfolio Selection," CEIS Research Paper 353, Tor Vergata University, CEIS, revised 07 Aug 2015.
    6. 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.
    7. 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.
    8. Yoshihiko Konno, 1991. "A note on estimating eigenvalues of scale matrix of the multivariate F-distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 157-165, March.
    9. Eckhard Liebscher & Wolf-Dieter Richter, 2016. "Estimation of Star-Shaped Distributions," Risks, MDPI, vol. 4(4), pages 1-37, November.
    10. 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.
    11. Battey, Heather & Linton, Oliver, 2014. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 43-67.
    12. Nabil Kazi-Tani & Didier Rullière, 2019. "On a construction of multivariate distributions given some multidimensional marginals," Post-Print hal-01575169, HAL.
    13. Klaus Müller & Wolf-Dieter Richter, 2019. "On p-generalized elliptical random processes," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-37, December.
    14. 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.
    15. Jeremias Leão & Francisco Cysneiros & Helton Saulo & N. Balakrishnan, 2016. "Constrained test in linear models with multivariate power exponential distribution," Computational Statistics, Springer, vol. 31(4), pages 1569-1592, December.
    16. 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.
    17. Heather Battey & Oliver Linton, 2013. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," CeMMAP working papers 15/13, Institute for Fiscal Studies.
    18. Fotopoulos, Stergios B., 2017. "Symmetric Gaussian mixture distributions with GGC scales," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 185-194.
    19. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
    20. 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.

    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:100:y:2009:i:4:p:742-752. 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.