IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v11y1981i3p319-333.html
   My bibliography  Save this article

Convergence systems and strong consistency of least squares estimates in regression models

Author

Listed:
  • Gui-Jing, Chen
  • Lai, T. L.
  • Wei, C. Z.

Abstract

A recent theorem of T. L. Hai, H. Robbins, and C. Z. Wei (J. Multivariate Anal. 9 (1979), 343-362) is extended to a more general form which unifies previous results in the literature on the strong consistency of least squares estimates in multiple regression models with nonrandom regressors. In particular the issue of strong consistency of the least squares estimate in the Gauss-Markov model, in the i.i.d. model with infinite second moment, and in general time series models is examined. In this connection, some basic properties of convergence systems are also obtained and are applied to the strong consistency problem.

Suggested Citation

  • Gui-Jing, Chen & Lai, T. L. & Wei, C. Z., 1981. "Convergence systems and strong consistency of least squares estimates in regression models," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 319-333, September.
    • Handle: RePEc:eee:jmvana:v:11:y:1981:i:3:p:319-333
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(81)90078-6
    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. Lita da Silva, João, 2014. "Some strong consistency results in stochastic regression," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 220-226.
    2. Marlene MUELLER, "undated". "Consistency properties of model selection criteria in multiple linear regression," Statistic und Oekonometrie 9207, Humboldt Universitaet Berlin.
    3. Wenzhi Yang & Haiyun Xu & Ling Chen & Shuhe Hu, 2018. "Complete consistency of estimators for regression models based on extended negatively dependent errors," Statistical Papers, Springer, vol. 59(2), pages 449-465, June.
    4. Ching-Kang Ing & Ching-Zong Wei, 2005. "A maximal moment inequality for long range dependent time series with applications to estimation and model selection," Econometrics 0508009, University Library of Munich, Germany.
    5. Aiting Shen & Yu Zhang & Benqiong Xiao & Andrei Volodin, 2017. "Moment inequalities for m-negatively associated random variables and their applications," Statistical Papers, Springer, vol. 58(3), pages 911-928, September.
    6. Bai, Z. D. & Guo, Meihui, 1999. "A paradox in least-squares estimation of linear regression models," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 167-174, April.
    7. Wu, Tiee-Jian & Wasan, M. T., 1996. "Weighted least squares estimates in linear regression models for processes with uncorrelated increments," Stochastic Processes and their Applications, Elsevier, vol. 64(2), pages 273-286, November.
    8. Dzhaparidze, K. & Spreij, P., 1989. "On SLLN for martingales with deterministic variation," Serie Research Memoranda 0079, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.

    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:11:y:1981:i:3:p:319-333. 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.