IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v202y2024ics0047259x23001288.html
   My bibliography  Save this article

Shrinkage estimators of BLUE for time series regression models

Author

Listed:
  • Xue, Yujie
  • Taniguchi, Masanobu
  • Liu, Tong

Abstract

The least squares estimator (LSE) seems a natural estimator of linear regression models. Whereas, if the dimension of the vector of regression coefficients is greater than 1 and the residuals are dependent, the best linear unbiased estimator (BLUE), which includes the information of the covariance matrix Γ of residual process has a better performance than LSE in the sense of mean square error. As we know the unbiased estimators are generally inadmissible, Senda and Taniguchi (2006) introduced a James–Stein type shrinkage estimator for the regression coefficients based on LSE, where the residual process is a Gaussian stationary process, and provides sufficient conditions such that the James–Stein type shrinkage estimator improves LSE. In this paper, we propose a shrinkage estimator based on BLUE. Sufficient conditions for this shrinkage estimator to improve BLUE are also given. Furthermore, since Γ is infeasible, assuming that Γ has a form of Γ=Γ(θ), we introduce a feasible version of that shrinkage estimator with replacing Γ(θ) by Γ(θˆ) which is introduced in Toyooka (1986). Additionally, we give the sufficient conditions where the feasible version improves BLUE. Besides, the results of a numerical studies confirm our approach.

Suggested Citation

  • Xue, Yujie & Taniguchi, Masanobu & Liu, Tong, 2024. "Shrinkage estimators of BLUE for time series regression models," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:jmvana:v:202:y:2024:i:c:s0047259x23001288
    DOI: 10.1016/j.jmva.2023.105282
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X23001288
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2023.105282?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:202:y:2024:i:c:s0047259x23001288. 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: 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.