IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2008i2p312-320.html
   My bibliography  Save this article

Improving updating rules in multiplicative algorithms for computing D-optimal designs

Author

Listed:
  • Dette, Holger
  • Pepelyshev, Andrey
  • Zhigljavsky, Anatoly

Abstract

A class of multiplicative algorithms for computing D-optimal designs for regression models on a finite design space is discussed and a monotonicity result for a sequence of determinants obtained by the iterations is proved. As a consequence the convergence of the sequence of designs to the D-optimal design is established. The class of algorithms is indexed by a real parameter and contains two algorithms considered previously as special cases. Numerical results are provided to demonstrate the efficiency of the proposed methods. Finally, several extensions to other optimality criteria are discussed.

Suggested Citation

  • Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2008. "Improving updating rules in multiplicative algorithms for computing D-optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 312-320, December.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:312-320
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00465-9
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pronzato, Luc, 2003. "Removing non-optimal support points in D-optimum design algorithms," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 223-228, July.
    2. D. M. Titterington, 1978. "Estimation of Correlation Coefficients by Ellipsoidal Trimming," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 27(3), pages 227-234, November.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Sahu, Nitesh & Babu, Prabhu, 2021. "A new monotonic algorithm for the E-optimal experiment design problem," Statistics & Probability Letters, Elsevier, vol. 174(C).
    4. Len Bos & Federico Piazzon & Marco Vianello, 2020. "Near G-optimal Tchakaloff designs," Computational Statistics, Springer, vol. 35(2), pages 803-819, June.
    5. Tim Holland-Letz & Holger Dette & Didier Renard, 2012. "Efficient Algorithms for Optimal Designs with Correlated Observations in Pharmacokinetics and Dose-Finding Studies," Biometrics, The International Biometric Society, vol. 68(1), pages 138-145, March.
    6. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2014. "‘Nearly’ universally optimal designs for models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1103-1112.
    7. Lucy L. Gao & Julie Zhou, 2017. "D-optimal designs based on the second-order least squares estimator," Statistical Papers, Springer, vol. 58(1), pages 77-94, March.
    8. 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.
    9. Tommasi, C. & López-Fidalgo, J., 2010. "Bayesian optimum designs for discriminating between models with any distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 143-150, January.
    10. Monica Dessole & Fabio Marcuzzi & Marco Vianello, 2020. "dCATCH—A Numerical Package for d-Variate near G-Optimal Tchakaloff Regression via Fast NNLS," Mathematics, MDPI, vol. 8(7), pages 1-15, July.
    11. Pronzato, Luc, 2013. "A delimitation of the support of optimal designs for Kiefer’s ϕp-class of criteria," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2721-2728.
    12. 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.
    13. Pierre Maréchal & Jane J. Ye & Julie Zhou, 2015. "K -Optimal Design via Semidefinite Programming and Entropy Optimization," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 495-512, February.
    14. 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.

    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. 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.
    2. 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.
    3. 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.
    4. Rosa, Samuel & Harman, Radoslav, 2022. "Computing minimum-volume enclosing ellipsoids for large datasets," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    5. 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.
    6. 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.
    7. Pronzato, Luc, 2013. "A delimitation of the support of optimal designs for Kiefer’s ϕp-class of criteria," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2721-2728.
    8. Karim Abou-Moustafa & Frank P. Ferrie, 2018. "Local generalized quadratic distance metrics: application to the k-nearest neighbors classifier," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 341-363, June.
    9. Peter Goos & Bradley Jones & Utami Syafitri, 2016. "I-Optimal Design of Mixture Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 899-911, April.
    10. Selin Ahipaşaoğlu, 2015. "Fast algorithms for the minimum volume estimator," Journal of Global Optimization, Springer, vol. 62(2), pages 351-370, June.
    11. 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.
    12. Nolan, D., 1999. "On min-max majority and deepest points," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 325-333, July.
    13. Belmiro P. M. Duarte & Weng Kee Wong, 2015. "Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach," International Statistical Review, International Statistical Institute, vol. 83(2), pages 239-262, August.
    14. Dolia, A.N. & Harris, C.J. & Shawe-Taylor, J.S. & Titterington, D.M., 2007. "Kernel ellipsoidal trimming," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 309-324, September.
    15. 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.
    16. Bernard, Carole & Vanduffel, Steven, 2015. "A new approach to assessing model risk in high dimensions," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 166-178.
    17. Beirlant, J. & Mason, D. M. & Vynckier, C., 1999. "Goodness-of-fit analysis for multivariate normality based on generalized quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 119-142, April.
    18. 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.
    19. 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.
    20. Pronzato, Luc, 2003. "Removing non-optimal support points in D-optimum design algorithms," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 223-228, July.

    More about this item

    Statistics

    Access and download statistics

    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:eee:csdana:v:53:y:2008:i:2:p:312-320. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.