IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2021i1p52-d710362.html
   My bibliography  Save this article

Comparison of Risk Ratios of Shrinkage Estimators in High Dimensions

Author

Listed:
  • Abdenour Hamdaoui

    (Department of Mathematics, University of Science and Technology of Oran-Mohamed Boudiaf (USTO-MB), Oran 31000, Algeria
    Laboratory of Statistics and Random Modelisations (LSMA), University Abou Bekr Belkaid, Tlemcen 13000, Algeria)

  • Waleed Almutiry

    (Department of Mathematics, College of Science and Arts in Ar Rass, Qassim University, Buryadah 52571, Saudi Arabia)

  • Mekki Terbeche

    (Department of Mathematics, University of Science and Technology of Oran-Mohamed Boudiaf (USTO-MB), Oran 31000, Algeria
    Laboratory of Analysis and Application of Radiation (LAAR), University of Science and Technology of Oran-Mohamed Boudiaf (USTO-MB), Oran 31000, Algeria)

  • Abdelkader Benkhaled

    (Department of Biology, University of Mascara, Mascara 29000, Algeria
    Laboratory of Stochastic Models, Statistics and Applications, University Tahar Moulay, Saida 20000, Algeria)

Abstract

In this paper, we analyze the risk ratios of several shrinkage estimators using a balanced loss function. The James–Stein estimator is one of a group of shrinkage estimators that has been proposed in the existing literature. For these estimators, sufficient criteria for minimaxity have been established, and the James–Stein estimator’s minimaxity has been derived. We demonstrate that the James–Stein estimator’s minimaxity is still valid even when the parameter space has infinite dimension. It is shown that the positive-part version of the James–Stein estimator is substantially superior to the James–Stein estimator, and we address the asymptotic behavior of their risk ratios to the maximum likelihood estimator (MLE) when the dimensions of the parameter space are infinite. Finally, a simulation study is carried out to verify the performance evaluation of the considered estimators.

Suggested Citation

  • Abdenour Hamdaoui & Waleed Almutiry & Mekki Terbeche & Abdelkader Benkhaled, 2021. "Comparison of Risk Ratios of Shrinkage Estimators in High Dimensions," Mathematics, MDPI, vol. 10(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2021:i:1:p:52-:d:710362
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/1/52/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/1/52/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:10:y:2021:i:1:p:52-:d:710362. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.