IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v162y2014i1d10.1007_s10957-013-0434-1.html
   My bibliography  Save this article

A Simple Proof of the Existence of the Best Estimator in a Quasilinear Regression Model

Author

Listed:
  • Dragan Jukić

    (J.J. Strossmayer University of Osijek)

Abstract

We provide a theorem on the existence of the best estimator in a quasilinear regression model, from which the existence of the best estimator for the whole class of nonlinear model functions follows immediately. The obtained theorem both extends and generalizes the previously known existence result. Our proof is elementary and rests on the basic knowledge of linear algebra and calculus.

Suggested Citation

  • Dragan Jukić, 2014. "A Simple Proof of the Existence of the Best Estimator in a Quasilinear Regression Model," Journal of Optimization Theory and Applications, Springer, vol. 162(1), pages 293-302, July.
  • Handle: RePEc:spr:joptap:v:162:y:2014:i:1:d:10.1007_s10957-013-0434-1
    DOI: 10.1007/s10957-013-0434-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0434-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-013-0434-1?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.

    References listed on IDEAS

    as
    1. E. Demidenko, 2008. "Criteria for Unconstrained Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 375-395, March.
    2. Demidenko, Eugene, 2006. "Criteria for global minimum of sum of squares in nonlinear regression," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1739-1753, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eugene Demidenko, 2017. "Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 636-665, September.
    2. Dragan Jukić & Kristian Sabo, 2021. "An existence criterion for the nonlinear $$\ell _p$$ ℓ p -norm fitting problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 957-966, September.
    3. Peng, Heng & Lu, Ying, 2012. "Model selection in linear mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 109-129.
    4. E. Demidenko, 2008. "Criteria for Unconstrained Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 375-395, March.
    5. Jukic, Dragan & Bensic, Mirta & Scitovski, Rudolf, 2008. "On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4502-4511, May.
    6. Gregory Cox, 2018. "Almost Sure Uniqueness of a Global Minimum Without Convexity," Papers 1803.02415, arXiv.org, revised Feb 2019.
    7. Antanas Žilinskas & Julius Žilinskas, 2013. "A hybrid global optimization algorithm for non-linear least squares regression," Journal of Global Optimization, Springer, vol. 56(2), pages 265-277, June.

    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:joptap:v:162:y:2014:i:1:d:10.1007_s10957-013-0434-1. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.