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

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  • 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.

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Pronzato, Luc, 2003. "Removing non-optimal support points in D-optimum design algorithms," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 223-228, July.
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    Cited by:

    1. 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.
    2. Len Bos & Federico Piazzon & Marco Vianello, 2020. "Near G-optimal Tchakaloff designs," Computational Statistics, Springer, vol. 35(2), pages 803-819, June.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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. 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.
    9. 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.
    10. 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.
    11. Sahu, Nitesh & Babu, Prabhu, 2021. "A new monotonic algorithm for the E-optimal experiment design problem," Statistics & Probability Letters, Elsevier, vol. 174(C).
    12. 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.
    13. 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.
    14. 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.

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