IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v85y2022i2d10.1007_s00184-021-00827-0.html
   My bibliography  Save this article

Minimax robust designs for regression models with heteroscedastic errors

Author

Listed:
  • Kai Yzenbrandt

    (University of Victoria)

  • Julie Zhou

    (University of Victoria)

Abstract

Minimax robust designs for regression models with heteroscedastic errors are studied and constructed. These designs are robust against possible misspecification of the error variance in the model. We propose a flexible assumption for the error variance and use a minimax approach to define robust designs. As usual it is hard to find robust designs analytically, since the associated design problem is not a convex optimization problem. However, we can show that the objective function of the minimax robust design problem is a difference of two convex functions. An effective algorithm is developed to compute minimax robust designs under the least squares estimator and generalized least squares estimator. The algorithm can be applied to construct minimax robust designs for any linear or nonlinear regression model with heteroscedastic errors. In addition, several theoretical results are obtained for the minimax robust designs.

Suggested Citation

  • Kai Yzenbrandt & Julie Zhou, 2022. "Minimax robust designs for regression models with heteroscedastic errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 203-222, February.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:2:d:10.1007_s00184-021-00827-0
    DOI: 10.1007/s00184-021-00827-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-021-00827-0
    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/s00184-021-00827-0?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. Linglong Kong & Douglas P. Wiens, 2015. "Model-Robust Designs for Quantile Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 233-245, March.
    2. Weng Kee Wong & Yue Yin & Julie Zhou, 2019. "Using SeDuMi to find various optimal designs for regression models," Statistical Papers, Springer, vol. 60(5), pages 1583-1603, October.
    3. Holger Dette & Weng Kee Wong, 1999. "Optimal Designs When the Variance Is A Function of the Mean," Biometrics, The International Biometric Society, vol. 55(3), pages 925-929, September.
    4. Fei Yan & Chongqi Zhang & Heng Peng, 2017. "Optimal designs for additive mixture model with heteroscedastic errors," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6401-6411, July.
    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. Mariano Amo-Salas & Jesús López-Fidalgo & Emilio Porcu, 2013. "Optimal designs for some stochastic processes whose covariance is a function of the mean," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 159-181, March.

    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:85:y:2022:i:2:d:10.1007_s00184-021-00827-0. 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.