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Elfving’s theorem for R-optimality of experimental designs

Author

Listed:
  • Xin Liu

    (Donghua University)

  • Rong-Xian Yue

    (Shanghai Normal University)

Abstract

The present paper is devoted to the construction of R-optimal designs in multiresponse linear models. The R-optimality criterion introduced by Dette (J R Stat Soc Ser B 59:97–110, 1997) minimizes the volume of Bonferroni rectangular confidence region for the parameter estimation. A generalization of Elfving’s theorem is proved for the optimal designs with respect to R-optimality, which gives a geometric characterization of R-optimal designs. The geometric characterizations of the R-optimal designs are illustrated by four examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:4:d:10.1007_s00184-019-00728-3
    DOI: 10.1007/s00184-019-00728-3
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    References listed on IDEAS

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    1. Tim Holland‐Letz & Holger Dette & Andrey Pepelyshev, 2011. "A geometric characterization of optimal designs for regression models with correlated observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 239-252, March.
    2. 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.
    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.
    4. 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.
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