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A note on $$R$$ -optimal designs for multiresponse models

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  • Xin Liu
  • Rong-Xian Yue

Abstract

This paper considers the optimal design problem for multiresponse regression models. The $$R$$ -optimality introduced by Dette (J R Stat Soc B 59:97–110, 1997 ) for single response experiments is extended to the case of multiresponse parameter estimation. A general equivalence theorem for the $$R$$ -optimality is provided for multiresponse models. Illustrative examples of the $$R$$ -optimal designs for two multiresponse models are presented based on the general equivalence theorem. Copyright Springer-Verlag 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:4:p:483-493
    DOI: 10.1007/s00184-012-0400-1
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    References listed on IDEAS

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    1. 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.
    2. Holger Dette, 1993. "A new interpretation of optimality forE-optimal designs in linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 37-50, December.
    3. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
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    Cited by:

    1. 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.
    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. Lei He & Rong-Xian Yue, 2020. "R-optimal designs for trigonometric regression models," Statistical Papers, Springer, vol. 61(5), pages 1997-2013, October.

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