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Excess and saturated D-optimal designs for the rational model

Author

Listed:
  • Yu. D. Grigoriev

    (St. Petersburg State Electrotechnical University)

  • V. B. Melas

    (St. Petersburg State University)

  • P. V. Shpilev

    (St. Petersburg State University)

Abstract

For a rational two-dimensional nonlinear in parameters model used in analytical chemistry, we investigate how homothetic transformations of the design space affect the number of support points in the optimal designs. We show that there exist two types of optimal designs: a saturated design (i.e. a design with the number of support points which is equal to the number of parameters) and an excess design (i.e. a design with the number of support points which is greater than the number of parameters). The optimal saturated designs are constructed explicitly. Numerical methods for constructing optimal excess designs are used.

Suggested Citation

  • Yu. D. Grigoriev & V. B. Melas & P. V. Shpilev, 2021. "Excess and saturated D-optimal designs for the rational model," Statistical Papers, Springer, vol. 62(3), pages 1387-1405, June.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:3:d:10.1007_s00362-019-01140-9
    DOI: 10.1007/s00362-019-01140-9
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    References listed on IDEAS

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    1. Yu. D. Grigoriev & V. B. Melas & P. V. Shpilev, 2018. "Excess of locally D-optimal designs for Cobb–Douglas model," Statistical Papers, Springer, vol. 59(4), pages 1425-1439, December.
    2. 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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