IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v83y2020i6d10.1007_s00184-019-00745-2.html
   My bibliography  Save this article

Locally D-optimal designs for heteroscedastic polynomial measurement error models

Author

Listed:
  • Min-Jue Zhang

    (Shanghai Normal University)

  • Rong-Xian Yue

    (Shanghai Normal University)

Abstract

This paper considers constructions of optimal designs for heteroscedastic polynomial measurement error models. Corresponding approximate design theory is developed by using corrected score function approach, which leads to non-concave optimisation problems. For the weighted polynomial measurement error model of degree p with some commonly used heteroscedastic structures, the upper bounds for the number of support points of locally D-optimal designs can be determined explicitly. A numerical example is given to show how heteroscedastic structures affect the optimal designs.

Suggested Citation

  • Min-Jue Zhang & Rong-Xian Yue, 2020. "Locally D-optimal designs for heteroscedastic polynomial measurement error models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 643-656, August.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:6:d:10.1007_s00184-019-00745-2
    DOI: 10.1007/s00184-019-00745-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-019-00745-2
    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/s00184-019-00745-2?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. Carmelo Rodríguez & Isabel Ortiz & Ignacio Martínez, 2016. "A-optimal designs for heteroscedastic multifactor regression models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(3), pages 757-771, February.
    2. Arturo Zavala & Heleno Bolfarine & Mário Castro, 2007. "Consistent estimation and testing in heteroscedastic polynomial errors-in-variables models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 515-530, September.
    3. Holger Dette & Matthias Trampisch, 2012. "Optimal Designs for Quantile Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1140-1151, September.
    4. M. Konstantinou & H. Dette, 2015. "Locally optimal designs for errors-in-variables models," Biometrika, Biometrika Trust, vol. 102(4), pages 951-958.
    5. Wong, Weng Kee, 1995. "On the equivalence of D and G-optimal designs in heteroscedastic models," Statistics & Probability Letters, Elsevier, vol. 25(4), pages 317-321, December.
    6. Lei He & Rong-Xian Yue, 2017. "R-optimal designs for multi-factor models with heteroscedastic errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 717-732, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Min-Jue Zhang & Rong-Xian Yue, 2021. "Optimal designs for homoscedastic functional polynomial measurement error models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 485-501, September.

    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. Lei He, 2021. "Bayesian optimal designs for multi-factor nonlinear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 223-233, March.
    2. Lei He & Rong-Xian Yue, 2017. "R-optimal designs for multi-factor models with heteroscedastic errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 717-732, November.
    3. Prus, Maryna, 2019. "Various optimality criteria for the prediction of individual response curves," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 36-41.
    4. 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.
    5. Lei He & Rong-Xian Yue, 2020. "R-optimal designs for trigonometric regression models," Statistical Papers, Springer, vol. 61(5), pages 1997-2013, October.
    6. Min-Jue Zhang & Rong-Xian Yue, 2021. "Optimal designs for homoscedastic functional polynomial measurement error models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 485-501, September.
    7. Peng, Cheng & Kouri, Drew P. & Uryasev, Stan, 2024. "Efficient and robust optimal design for quantile regression based on linear programming," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    8. He, Lei, 2018. "Optimal designs for multi-factor nonlinear models based on the second-order least squares estimator," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 201-208.
    9. Xin Liu & Rong-Xian Yue, 2020. "Elfving’s theorem for R-optimality of experimental designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(4), pages 485-498, May.

    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:83:y:2020:i:6:d:10.1007_s00184-019-00745-2. 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.