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A delimitation of the support of optimal designs for Kiefer’s ϕp-class of criteria

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  • Pronzato, Luc

Abstract

The paper extends the result of Harman and Pronzato [Harman, R., Pronzato, L., 2007. Improvements on removing non-optimal support points in D-optimum design algorithms. Statistics & Probability Letters 77, 90–94], which corresponds to p=0, to all strictly concave criteria in Kiefer’s ϕp-class. We show that, for any given design measure ξ, any support point x∗ of a ϕp-optimal design is such that the directional derivative of ϕp at ξ in the direction of the delta measure at x∗ is larger than some bound hp[ξ] which is easily computed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:12:p:2721-2728
    DOI: 10.1016/j.spl.2013.09.009
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    References listed on IDEAS

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    1. Leonid G. Khachiyan, 1996. "Rounding of Polytopes in the Real Number Model of Computation," Mathematics of Operations Research, INFORMS, vol. 21(2), pages 307-320, May.
    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. 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. Pronzato, Luc, 2003. "Removing non-optimal support points in D-optimum design algorithms," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 223-228, July.
    5. 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.
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    Cited by:

    1. Guillaume Sagnol & Edouard Pauwels, 2019. "An unexpected connection between Bayes A-optimal designs and the group lasso," Statistical Papers, Springer, vol. 60(2), pages 565-584, April.
    2. Gauthier, B. & Pronzato, L., 2017. "Convex relaxation for IMSE optimal design in random-field models," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 375-394.
    3. Rosa, Samuel & Harman, Radoslav, 2022. "Computing minimum-volume enclosing ellipsoids for large datasets," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    4. 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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