IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v42y1992i1p130-140.html
   My bibliography  Save this article

D-Optimal designs for a multivariate regression model

Author

Listed:
  • Krafft, Olaf
  • Schaefer, Martin

Abstract

Considered is a linear regression model with a one-dimensional control variable and an m-dimensional response variable y. The components of y may be correlated with known covariance matrix. Let B be the covariance matrix of the Gauss-Markoff estimator for the unknown parameter vector of the model. Under rather mild assumptions on the set of regression functions a factorization lemma for det B is proved which implies that D-optimal designs do not depend on the covariance matrix of y. This allows the use of recent results of Dette to determine approximate D-optimal designs for polynomial regression. A partial result for exact D-optimal designs is given too.

Suggested Citation

  • Krafft, Olaf & Schaefer, Martin, 1992. "D-Optimal designs for a multivariate regression model," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 130-140, July.
    • Handle: RePEc:eee:jmvana:v:42:y:1992:i:1:p:130-140
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(92)90083-R
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Idais, Osama, 2020. "Locally optimal designs for multivariate generalized linear models," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    2. Imhof, Lorens, 2000. "Optimum Designs for a Multiresponse Regression Model," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 120-131, January.
    3. Xin Liu & Rong-Xian Yue, 2013. "A note on $$R$$ -optimal designs for multiresponse models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 483-493, May.
    4. Yue, Rong-Xian & Liu, Xin, 2010. "-optimal designs for a hierarchically ordered system of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3458-3465, December.
    5. Wolfgang Bischoff, 1995. "Determinant formulas with applications to designing when the observations are correlated," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(2), pages 385-399, June.
    6. Lin, Chun-Sui & Huang, Mong-Na Lo, 2010. "Optimal designs for estimating the control values in multi-univariate regression models," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1055-1066, May.
    7. Katarzyna Filipiak & Augustyn Markiewicz & Anna Szczepańska, 2009. "Optimal designs under a multivariate linear model with additional nuisance parameters," Statistical Papers, Springer, vol. 50(4), pages 761-778, August.
    8. Yue, Rong-Xian & Liu, Xin & Chatterjee, Kashinath, 2014. "D-optimal designs for multiresponse linear models with a qualitative factor," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 57-69.
    9. Kao, Ming-Hung & Khogeer, Hazar, 2021. "Optimal designs for mixed continuous and binary responses with quantitative and qualitative factors," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    10. Han, Cong, 2003. "A note on optimal designs for a two-part model," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 343-351, December.
    11. Konrad Engel & Sylke Gierer, 1993. "Optimal designs for models with block-block resp. treatment-treatment correlations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 349-359, December.
    12. Yue, Rong-Xian, 2002. "Model-robust designs in multiresponse situations," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 369-379, July.

    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:eee:jmvana:v:42:y:1992:i:1:p:130-140. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.