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Multiplication Algorithms for Approximate Optimal Distributions with Cost Constraints

Author

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  • Lianyan Fu

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China
    These authors contributed equally to this work.)

  • Faming Ma

    (School of Economics, Liaoning University, Shenyang 110036, China
    These authors contributed equally to this work.)

  • Zhuoxi Yu

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China)

  • Zhichuan Zhu

    (School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China)

Abstract

In this paper, we study the D - and A -optimal assignment problems for regression models with experimental cost constraints. To solve these two problems, we propose two multiplicative algorithms for obtaining optimal designs and establishing extended D -optimal ( E D -optimal) and A -optimal ( E A -optimal) criteria. In addition, we give proof of the convergence of the E D -optimal algorithm and draw conjectures about some properties of the E A -optimal algorithm. Compared with the classical D - and A -optimal algorithms, the E D - and E A -optimal algorithms consider not only the accuracy of parameter estimation, but also the experimental cost constraint. The proposed methods work well in the digital example.

Suggested Citation

  • Lianyan Fu & Faming Ma & Zhuoxi Yu & Zhichuan Zhu, 2023. "Multiplication Algorithms for Approximate Optimal Distributions with Cost Constraints," Mathematics, MDPI, vol. 11(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1963-:d:1129108
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    References listed on IDEAS

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    1. Steven G. Gilmour & Luzia A. Trinca, 2012. "Optimum design of experiments for statistical inference," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(3), pages 345-401, May.
    2. Martin-Martin, R. & Torsney, B. & Lopez-Fidalgo, J., 2007. "Construction of marginally and conditionally restricted designs using multiplicative algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5547-5561, August.
    3. Radoslav Harman & Alena Bachratá & Lenka Filová, 2016. "Construction of efficient experimental designs under multiple resource constraints," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(1), pages 3-17, January.
    4. Harman, Radoslav & Pronzato, Luc, 2007. "Improvements on removing nonoptimal support points in D-optimum design algorithms," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 90-94, January.
    5. Min Yang & Stefanie Biedermann & Elina Tang, 2013. "On Optimal Designs for Nonlinear Models: A General and Efficient Algorithm," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1411-1420, December.
    6. Radoslav Harman & Lenka Filová & Peter Richtárik, 2020. "A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 348-361, January.
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