IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v59y2004i1p75-97.html
   My bibliography  Save this article

Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model AX=B

Author

Listed:
  • Alexander Kukush
  • Sabine Van Huffel

Abstract

A multivariate measurement error model AX≈B is considered. The errors in [A,B] are rowwise independent, but within each row the errors may be correlated. Some of the columns are observed without errors, and in addition the error covariance matrices may differ from row to row. The total covariance structure of the errors is supposed to be known up to a scalar factor. The fully weighted total least squares estimator of X is studied, which in the case of normal errors coincides with the maximum likelihood estimator. We give mild conditions for weak and strong consistency of the estimator, when the number of rows in A increases. The results generalize the conditions of Gallo given for a univariate homoscedastic model (where B is a vector), and extend the conditions of Gleser given for the multivariate homoscedastic model. We derive the objective function for the estimator and propose an iteratively reweighted numerical procedure. Copyright Springer-Verlag 2004

Suggested Citation

  • Alexander Kukush & Sabine Van Huffel, 2004. "Consistency of elementwise-weighted total least squares estimator in a multivariate errors-in-variables model AX=B," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 75-97, February.
    • Handle: RePEc:spr:metrik:v:59:y:2004:i:1:p:75-97
    DOI: 10.1007/s001840300272
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s001840300272
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s001840300272?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.

    Citations

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


    Cited by:

    1. de Castro, Mario & Galea-Rojas, Manuel & Bolfarine, Heleno, 2007. "Local influence assessment in heteroscedastic measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1132-1142, October.
    2. Markovsky, Ivan & Luisa Rastello, Maria & Premoli, Amedeo & Kukush, Alexander & Van Huffel, Sabine, 2006. "The element-wise weighted total least-squares problem," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 181-209, January.
    3. Milan Hladík & Michal Černý & Jaromír Antoch, 2020. "EIV regression with bounded errors in data: total ‘least squares’ with Chebyshev norm," Statistical Papers, Springer, vol. 61(1), pages 279-301, February.
    4. Kukush, A. & Markovsky, I. & Van Huffel, S., 2007. "Estimation in a linear multivariate measurement error model with a change point in the data," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1167-1182, October.
    5. Michal Pešta, 2016. "Unitarily invariant errors-in-variables estimation," Statistical Papers, Springer, vol. 57(4), pages 1041-1057, December.

    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:spr:metrik:v:59:y:2004:i:1:p:75-97. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.