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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
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    Citations

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    Cited by:

    1. Idais, Osama, 2020. "Locally optimal designs for multivariate generalized linear models," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    2. 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).
    3. 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.
    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. Han, Cong, 2003. "A note on optimal designs for a two-part model," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 343-351, December.
    6. Imhof, Lorens, 2000. "Optimum Designs for a Multiresponse Regression Model," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 120-131, January.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Yue, Rong-Xian, 2002. "Model-robust designs in multiresponse situations," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 369-379, July.

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