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Improvements on removing nonoptimal support points in D-optimum design algorithms

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  • Harman, Radoslav
  • Pronzato, Luc

Abstract

We improve the inequality used in Pronzato [2003. Removing non-optimal support points in D-optimum design algorithms. Statist. Probab. Lett. 63, 223-228] to remove points from the design space during the search for a D-optimum design. Let [xi] be any design on a compact space with a nonsingular information matrix, and let m+[epsilon] be the maximum of the variance function d([xi],x) over all . We prove that any support point x* of a D-optimum design on must satisfy the inequality . We show that this new lower bound on d([xi],x*) is, in a sense, the best possible, and how it can be used to accelerate algorithms for D-optimum design.

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  • 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.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:1:p:90-94
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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. 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. Selin Ahipaşaoğlu, 2015. "Fast algorithms for the minimum volume estimator," Journal of Global Optimization, Springer, vol. 62(2), pages 351-370, June.
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Rosa, Samuel & Harman, Radoslav, 2022. "Computing minimum-volume enclosing ellipsoids for large datasets," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    12. 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.
    13. 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.

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