IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v68y1999i2p176-192.html
   My bibliography  Save this article

Improving on the Best Affine Equivariant Estimator of the Ratio of Generalized Variances

Author

Listed:
  • Iliopoulos, George
  • Kourouklis, Stavros

Abstract

We consider the problem of decision-theoretic estimation of the ratio of generalized variances of two matrix normal distributions with unknown means under a general loss function. The inadmissibility of the best affine equivariant estimator is established by exhibiting various improved estimators. In particular, under certain conditions on the loss, two classes of improved procedures based onallthe available data are presented. As a preliminary result of independent interest, an improved estimator of an arbitrary power of the generalized variance of a matrix normal distribution with an unknown mean is derived under a general strictly bowl-shaped loss.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:68:y:1999:i:2:p:176-192
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(98)91790-0
    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. Sinha, Bimal Kumar, 1976. "On improved estimators of the generalized variance," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 617-625, December.
    2. 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.
    3. Tatsuya Kubokawa & Yoshihiko Konno, 1990. "Estimating the covariance matrix and the generalized variance under a symmetric loss," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 331-343, June.
    4. 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.
    5. SenGupta, Ashis, 1987. "Tests for standardized generalized variances of multivariate normal populations of possibly different dimensions," Journal of Multivariate Analysis, Elsevier, vol. 23(2), pages 209-219, December.
    6. Ghosh M. & Sinha B. K., 1987. "Inadmissibility Of The Best Equivariant Estimators Of The Variance-Covariance Matrix, The Precision Matrix, And The Generalized Variance Under Entropy Loss," Statistics & Risk Modeling, De Gruyter, vol. 5(3-4), pages 201-228, April.
    7. Ram Tripathi & Ramesh Gupta & John Gurland, 1994. "Estimation of parameters in the beta binomial model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 317-331, June.
    8. Ghosh M. & Kundu S., 1996. "Decision Theoretic Estimation Of The Variance Ratio," Statistics & Risk Modeling, De Gruyter, vol. 14(2), pages 161-176, February.
    9. Tatsuya Kubokawa, 1994. "Double shrinkage estimation of ratio of scale parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 95-116, 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. George Iliopoulos, 2001. "Decision Theoretic Estimation of the Ratio of Variances in a Bivariate Normal Distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 436-446, September.
    2. Iliopoulos G. & Kourouklis S., 2000. "Interval Estimation For The Ratio Of Scale Parameters And For Ordered Scale Parameters," Statistics & Risk Modeling, De Gruyter, vol. 18(2), pages 169-184, February.
    3. Iliopoulos, George, 2000. "A note on decision theoretic estimation of ordered parameters," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 33-38, October.
    4. Constantinos Petropoulos, 2017. "Estimation of the order restricted scale parameters for two populations from the Lomax distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(4), pages 483-502, May.
    5. 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.
    6. Panayiotis Bobotas & George Iliopoulos & Stavros Kourouklis, 2012. "Estimating the ratio of two scale parameters: a simple approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 343-357, April.

    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. 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.
    2. 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.
    3. Panayiotis Bobotas & George Iliopoulos & Stavros Kourouklis, 2012. "Estimating the ratio of two scale parameters: a simple approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 343-357, April.
    4. Misra, Neeraj & Singh, Harshinder & Demchuk, Eugene, 2005. "Estimation of the entropy of a multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 324-342, February.
    5. 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.
    6. Tatsuya Kubokawa, 2013. "General Dominance Properties of Double Shrinkage Estimators for Ratio of Positive Parameters," CIRJE F-Series CIRJE-F-901, CIRJE, Faculty of Economics, University of Tokyo.
    7. Dariush Najarzadeh, 2019. "Testing equality of standardized generalized variances of k multivariate normal populations with arbitrary dimensions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 593-623, December.
    8. 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.
    9. Iliopoulos G. & Kourouklis S., 2000. "Interval Estimation For The Ratio Of Scale Parameters And For Ordered Scale Parameters," Statistics & Risk Modeling, De Gruyter, vol. 18(2), pages 169-184, February.
    10. Maria Iannario, 2015. "Detecting latent components in ordinal data with overdispersion by means of a mixture distribution," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 977-987, May.
    11. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    12. Nariaki Sugiura & Yoshihiko Konno, 1988. "Entropy loss and risk of improved estimators for the generalized variance and precision," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(2), pages 329-341, June.
    13. Aubry, Philippe & Francesiaz, Charlotte & Guillemain, Matthieu, 2024. "On the impact of preferential sampling on ecological status and trend assessment," Ecological Modelling, Elsevier, vol. 492(C).
    14. Pronzato, Luc & Wynn, Henry P. & Zhigljavsky, Anatoly A., 2018. "Simplicial variances, potentials and Mahalanobis distances," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 276-289.
    15. Bhandary, Madhusudan, 1996. "Test for generalized variance in signal processing," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 155-162, April.
    16. Grace Weishi Gu & Zachary R. Stangebye, 2023. "Costly Information And Sovereign Risk," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(4), pages 1397-1429, November.
    17. He, Daojiang & Xu, Kai, 2014. "Estimation of the Cholesky decomposition in a conditional independent normal model with missing data," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 27-39.
    18. Hekimoğlu, Mustafa & Karlı, Deniz, 2023. "Modeling repair demand in existence of a nonstationary installed base," International Journal of Production Economics, Elsevier, vol. 263(C).
    19. Ledoit, Olivier & Wolf, Michael, 2021. "Shrinkage estimation of large covariance matrices: Keep it simple, statistician?," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    20. Constantinos Petropoulos & Stavros Kourouklis, 2012. "New classes of improved confidence intervals for the variance of a normal distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(4), pages 491-506, May.

    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:68:y:1999:i:2:p:176-192. 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.