IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2013cf901.html
   My bibliography  Save this paper

General Dominance Properties of Double Shrinkage Estimators for Ratio of Positive Parameters

Author

Listed:
  • Tatsuya Kubokawa

    (Faculty of Economics, University of Tokyo)

Abstract

   In estimation of ratio of variances in two normal distributions with unknown means, it has been shown in the literature that simple and crude ratio estimators based on two sample variances are dominated by shrinkage estimators using information contained in sample means. Of these, a natural double shrinkage estimator is the ratio of shrinkage estimators of variances, but its improvement over the crude ratio estimator depends on loss functions, namely, the improvement has not been established except the Stein loss function. In this paper, this dominance property is shown for some convex loss functions including the Stein and quadratic loss functions in the general framework of distributions with positive parameters and shrinkage estimators. The resulting new finding is that the generalized Bayes estimator of the ratio of variances dominates the crude ratio estimator relative to the quadratic loss. The paper also shows that the dominance property of the double shrinkage estimator holds for estimation of the difference of variances, but it does not hold for estimation of the product and sum of variances. Finally, it is demonstrated that the double shrinkage estimators for the ratio, product, sum and differences of variances are connected to estimation of linear combinations of the normal positive means, and the dominance and non-dominance results of the double shrinkage estimators coincide with the corresponding dominance results in estimation of linear combinations of means.

Suggested Citation

  • 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.
  • Handle: RePEc:tky:fseres:2013cf901
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2013/2013cf901.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ghosh M. & Kundu S., 1996. "Decision Theoretic Estimation Of The Variance Ratio," Statistics & Risk Modeling, De Gruyter, vol. 14(2), pages 161-176, February.
    2. Andrew Rukhin, 1992. "Asymptotic risk behavior of mean vector and variance estimators and the problem of positive normal mean," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(2), pages 299-311, June.
    3. 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.
    4. 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.
    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. Tatsuya Kubokawa, 2010. "Minimax Estimation of Linear Combinations of Restricted Location Parameters," CIRJE F-Series CIRJE-F-723, CIRJE, Faculty of Economics, University of Tokyo.
    2. 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.
    3. 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.
    4. 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.
    5. D. Kim & S. Kang & W. Lee, 2009. "Noninformative priors for the normal variance ratio," Statistical Papers, Springer, vol. 50(2), pages 393-402, March.
    6. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E. & Turcotte, Jean-Philippe, 2013. "Minimaxity in predictive density estimation with parametric constraints," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 382-397.
    7. Tatsuya Kubokawa & Éric Marchand & William E. Strawderman & Jean-Philippe Turcotte, 2012. "Minimaxity in Predictive Density Estimation with Parametric Constraints," CIRJE F-Series CIRJE-F-843, CIRJE, Faculty of Economics, University of Tokyo.
    8. van Eeden, Constance & V. Zidek, James, 2001. "Estimating one of two normal means when their difference is bounded," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 277-284, February.
    9. Iliopoulos, George, 2000. "A note on decision theoretic estimation of ordered parameters," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 33-38, October.
    10. Lakshmi Kanta Patra & Suchandan Kayal & Somesh Kumar, 2020. "Estimating a function of scale parameter of an exponential population with unknown location under general loss function," Statistical Papers, Springer, vol. 61(6), pages 2511-2527, December.
    11. 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.

    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:2013cf901. 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.