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Removing non-optimal support points in D-optimum design algorithms

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  • Pronzato, Luc

Abstract

We show that points can be removed from the design space during the search for a D-optimum design, using a simple inequality satisfied by support points of a D-optimum design measure. This inequality does not seem to have been noticed before but may be used for accelerating algorithms for D-optimum design, or for the determination of minimum covering ellipsoids, as used, e.g., in ellipsoidal trimming.

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  • Pronzato, Luc, 2003. "Removing non-optimal support points in D-optimum design algorithms," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 223-228, July.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:3:p:223-228
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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. Cook, R. D. & Hawkins, D. M. & Weisberg, S., 1993. "Exact iterative computation of the robust multivariate minimum volume ellipsoid estimator," Statistics & Probability Letters, Elsevier, vol. 16(3), pages 213-218, February.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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. 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.
    6. 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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