IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v30y2021i1d10.1007_s10260-020-00522-w.html
   My bibliography  Save this article

Bayesian optimal designs for multi-factor nonlinear models

Author

Listed:
  • Lei He

    (Anhui Normal University)

Abstract

This article is concerned with the Bayesian optimal design problem for multi-factor nonlinear models. In particular, the Bayesian $$\varPsi _q$$ Ψ q -optimality criterion proposed by Dette et al. (Stat Sinica 17:463–480, 2007) is considered. It is shown that the product-type designs are optimal for the additive multi-factor nonlinear models with or without constant term when the proposed sufficient conditions are satisfied. Some examples of application using the exponential growth models with several variables are presented to illustrate optimal designs based on the Bayesian $$\varPsi _q$$ Ψ q -optimality criterion considered.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:1:d:10.1007_s10260-020-00522-w
    DOI: 10.1007/s10260-020-00522-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-020-00522-w
    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/s10260-020-00522-w?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. 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.
    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. 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.
    4. S. Biedermann & H. Dette & D. C. Woods, 2011. "Optimal design for additive partially nonlinear models," Biometrika, Biometrika Trust, vol. 98(2), pages 449-458.
    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. 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.
    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. 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.
    4. Lei He & Rong-Xian Yue, 2020. "R-optimal designs for trigonometric regression models," Statistical Papers, Springer, vol. 61(5), pages 1997-2013, October.
    5. Thomas Schaubroeck & Simon Schaubroeck & Reinout Heijungs & Alessandra Zamagni & Miguel Brandão & Enrico Benetto, 2021. "Attributional & Consequential Life Cycle Assessment: Definitions, Conceptual Characteristics and Modelling Restrictions," Sustainability, MDPI, vol. 13(13), pages 1-47, July.
    6. Rui Li & Yuanyuan Zhang, 2021. "Two-stage estimation and simultaneous confidence band in partially nonlinear additive model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1109-1140, November.
    7. Lei He & Rong-Xian Yue, 2022. "$$I_L$$ I L -optimal designs for regression models under the second-order least squares estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 53-66, January.
    8. 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:stmapp:v:30:y:2021:i:1:d:10.1007_s10260-020-00522-w. 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.