IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v27y1988i1p116-130.html
   My bibliography  Save this article

Strong consistency of M-estimates in linear models

Author

Listed:
  • Chen, X. R.
  • Wu, Y. H.

Abstract

This article studies the strong consistency of M-estimates in linear regression models directly from the minimization problem 75, where X1. X2, ... can be random observations of a p-dimensional random vector X, or that they are simply known nonrandom p-vectors. It is shown that the solution ([alpha]n, [beta]'n) of this minimization problem converges with probability one to the true parameter ([alpha]0,[beta]'0) under very general conditions on the function [varrho] and the sequence {(X'i, Yi)}.

Suggested Citation

  • Chen, X. R. & Wu, Y. H., 1988. "Strong consistency of M-estimates in linear models," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 116-130, October.
  • Handle: RePEc:eee:jmvana:v:27:y:1988:i:1:p:116-130
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(88)90120-0
    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. Bai, Z. D. & Wu, Y., 1997. "On necessary conditions for the weak consistency of minimum L1-norm estimates in linear models," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 193-199, June.
    2. Søren Johansen & Bent Nielsen, 2014. "Outlier detection algorithms for least squares time series regression," Economics Papers 2014-W04, Economics Group, Nuffield College, University of Oxford.
    3. Søren Johansen & Bent Nielsen, 2016. "Tightness of M-estimators for multiple linear regression in time for multiple linear regression in time series," Discussion Papers 16-05, University of Copenhagen. Department of Economics.
    4. Xin Deng & Xuejun Wang, 2018. "Asymptotic Property of M Estimator in Classical Linear Models Under Dependent Random Errors," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1069-1090, December.
    5. Søren Johansen & Bent Nielsen, 2016. "Tightness of M-estimators for multiple linear regression in time series," CREATES Research Papers 2016-18, Department of Economics and Business Economics, Aarhus University.
    6. Lukasz Gatarek & Søren Johansen, 2014. "Optimal hedging with the cointegrated vector autoregressive model," Discussion Papers 14-22, University of Copenhagen. Department of Economics.
    7. Søren Johansen & Bent Nielsen, 2016. "Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 321-348, June.
    8. Xin Deng & Xuejun Wang, 2020. "An exponential inequality and its application to M estimators in multiple linear models," Statistical Papers, Springer, vol. 61(4), pages 1607-1627, August.

    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:27:y:1988:i:1:p:116-130. 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.