IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i8p1963-d1129108.html
   My bibliography  Save this article

Multiplication Algorithms for Approximate Optimal Distributions with Cost Constraints

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/8/1963/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/8/1963/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rosa, Samuel & Harman, Radoslav, 2022. "Computing minimum-volume enclosing ellipsoids for large datasets," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    2. Duarte, Belmiro P.M. & Atkinson, Anthony C. & Granjo, Jose F.O & Oliveira, Nuno M.C, 2019. "Optimal design of experiments for liquid–liquid equilibria characterization via semidefinite programming," LSE Research Online Documents on Economics 102500, London School of Economics and Political Science, LSE Library.
    3. Haoyu Wang & Chongqi Zhang, 2022. "The mixture design threshold accepting algorithm for generating $$\varvec{D}$$ D -optimal designs of the mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(3), pages 345-371, April.
    4. Lenka Filová & Radoslav Harman, 2020. "Ascent with quadratic assistance for the construction of exact experimental designs," Computational Statistics, Springer, vol. 35(2), pages 775-801, June.
    5. García-Ródenas, Ricardo & García-García, José Carlos & López-Fidalgo, Jesús & Martín-Baos, José Ángel & Wong, Weng Kee, 2020. "A comparison of general-purpose optimization algorithms for finding optimal approximate experimental designs," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    6. Radoslav Harman & Eva Benková, 2017. "Barycentric algorithm for computing D-optimal size- and cost-constrained designs of experiments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 201-225, February.
    7. Duarte, Belmiro P.M. & Atkinson, Anthony C. & Granjo, Jose F.O & Oliveira, Nuno M.C, 2022. "Optimal design of experiments for implicit models," LSE Research Online Documents on Economics 107584, London School of Economics and Political Science, LSE Library.
    8. Yu, Jun & Meng, Xiran & Wang, Yaping, 2023. "Optimal designs for semi-parametric dose-response models under random contamination," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    9. Àngela Sebastià Bargues & José-Luis Polo Sanz & Raúl Martín Martín, 2022. "Optimal Experimental Design for Parametric Identification of the Electrical Behaviour of Bioelectrodes and Biological Tissues," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
    10. Harman, Radoslav & Rosa, Samuel, 2019. "Removal of the points that do not support an E-optimal experimental design," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 83-89.
    11. Víctor Casero-Alonso & Jesús López-Fidalgo, 2015. "Experimental designs in triangular simultaneous equations models," Statistical Papers, Springer, vol. 56(2), pages 273-290, May.
    12. Duarte, Belmiro P.M. & Sagnol, Guillaume & Wong, Weng Kee, 2018. "An algorithm based on semidefinite programming for finding minimax optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 99-117.
    13. Selin Ahipaşaoğlu, 2015. "Fast algorithms for the minimum volume estimator," Journal of Global Optimization, Springer, vol. 62(2), pages 351-370, June.
    14. da Silva, Marcelo A. & Gilmour, Steven G. & Trinca, Luzia A., 2017. "Factorial and response surface designs robust to missing observations," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 261-272.
    15. Smucker, Byran J. & Castillo, Enrique del & Rosenberger, James L., 2012. "Model-robust designs for split-plot experiments," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4111-4121.
    16. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2007. "Improving updating rules in multiplicativealgorithms for computing D-optimal designs," Technical Reports 2007,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    17. Belmiro P. M. Duarte, 2023. "Exact Optimal Designs of Experiments for Factorial Models via Mixed-Integer Semidefinite Programming," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    18. López-Fidalgo, J. & Rivas-López, M.J., 2014. "Optimal experimental designs for partial likelihood information," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 859-867.
    19. Jacopo Paglia & Jo Eidsvik & Juha Karvanen, 2022. "Efficient spatial designs using Hausdorff distances and Bayesian optimization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1060-1084, September.
    20. Yu, Yaming, 2010. "Strict monotonicity and convergence rate of Titterington's algorithm for computing D-optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1419-1425, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1963-:d:1129108. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.