IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v57y1995i1p167-189.html
   My bibliography  Save this article

Bahadur-Kiefer representations for GM-estimators in autoregression models

Author

Listed:
  • Koul, Hira L.
  • Zhu, Zhiwei

Abstract

This paper proves strong consistency, along with a rate, of a class of generalized M-estimators for the autoregression parameter vector in pth order autoregression (AR(p)) models. If the score function [psi] has bounded second derivative then the rate of convergence is n-1/2(lnlnn)1/2 while for a general [psi] it is n-1/2(lnn)1/2. The paper also obtains the Bahadur-Kiefer type representations for these estimators. The class of estimators covered includes the least square, the least absolute deviation, and the Huber(k) estimators.

Suggested Citation

  • Koul, Hira L. & Zhu, Zhiwei, 1995. "Bahadur-Kiefer representations for GM-estimators in autoregression models," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 167-189, May.
    • Handle: RePEc:eee:spapps:v:57:y:1995:i:1:p:167-189
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(95)00008-U
    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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liebscher, Eckhard, 2003. "Strong convergence of estimators in nonlinear autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 247-261, February.
    2. Sinha, Sanjoy K. & Field, Christopher A. & Smith, Bruce, 2003. "Robust estimation of nonlinear regression with autoregressive errors," Statistics & Probability Letters, Elsevier, vol. 63(1), pages 49-59, May.
    3. Cheng, Fuxia, 2018. "Glivenko–Cantelli Theorem for the kernel error distribution estimator in the first-order autoregressive model," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 95-102.

    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:spapps:v:57:y:1995:i:1:p:167-189. 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/505572/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.