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Equivalence of weighted and partial optimality of experimental designs

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  • Samuel Rosa

    (Comenius University in Bratislava)

Abstract

The recently introduced weighted optimality criteria for experimental designs allow one to place various emphasis on different parameters or functions of parameters of interest. However, various emphasis on parameter functions can also be expressed by considering the well-developed optimality criteria for estimating a parameter system of interest (the partial optimality criteria). We prove that the approaches of weighted optimality and of partial optimality are in fact equivalent for any eigenvalue-based optimality criterion. This opens up the possibility to use the large body of existing theoretical and computational results for the partial optimality to derive theorems and numerical algorithms for the weighted optimality of experimental designs. We demonstrate the applicability of the proven equivalence on a few examples. We also propose a slight generalization of the weighted optimality so that it can represent the experimental objective consisting of any system of linear estimable functions.

Suggested Citation

  • Samuel Rosa, 2019. "Equivalence of weighted and partial optimality of experimental designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 719-732, August.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:6:d:10.1007_s00184-019-00706-9
    DOI: 10.1007/s00184-019-00706-9
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    References listed on IDEAS

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    1. Morgan, John P. & Wang, Xiaowei, 2010. "Weighted Optimality in Designed Experimentation," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1566-1580.
    2. J. W. Stallings & J. P. Morgan, 2015. "General weighted optimality of designed experiments," Biometrika, Biometrika Trust, vol. 102(4), pages 925-935.
    3. Samuel Rosa & Radoslav Harman, 2017. "Optimal approximate designs for comparison with control in dose-escalation studies," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 638-660, September.
    4. Samuel Rosa & Radoslav Harman, 2016. "Optimal approximate designs for estimating treatment contrasts resistant to nuisance effects," Statistical Papers, Springer, vol. 57(4), pages 1077-1106, December.
    5. Samuel Rosa, 2018. "Optimal designs for treatment comparisons represented by graphs," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 479-503, October.
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