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Efficiencies of Rounded Optimal Approximate Designs for Small Samples

Author

Listed:
  • L. Imhof
  • J. Lopez‐Fidalgo
  • W. K. Wong

Abstract

Optimal exact designs are notoriously hard to study and only a few of them are known for polynomial models. Using recently obtained optimal exact designs (Imhof, 1997), we show that the efficiency of the frequently used rounded optimal approximate designs can be sensitive if the sample size is small. For some criteria, the efficiency of the rounded optimal approximate design can vary by as much as 25% when the sample size is changed by one unit. The paper also discusses lower efficiency bounds and shows that they are sometimes the best possible bounds for the rounded optimal approximate designs.

Suggested Citation

  • L. Imhof & J. Lopez‐Fidalgo & W. K. Wong, 2001. "Efficiencies of Rounded Optimal Approximate Designs for Small Samples," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(3), pages 301-318, November.
    • Handle: RePEc:bla:stanee:v:55:y:2001:i:3:p:301-318
    DOI: 10.1111/1467-9574.00171
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    Cited by:

    1. Harman, Radoslav & Filová, Lenka, 2014. "Computing efficient exact designs of experiments using integer quadratic programming," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1159-1167.
    2. Àngela Sebastià Bargues & José-Luis Polo Sanz & Raúl Martín Martín, 2022. "Optimal Experimental Design for Parametric Identification of the Electrical Behaviour of Bioelectrodes and Biological Tissues," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
    3. Víctor Casero-Alonso & Jesús López-Fidalgo, 2015. "Optimal designs subject to cost constraints in simultaneous equations models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 701-713, December.
    4. Singh, Satya Prakash & Davidov, Ori, 2021. "On efficient exact experimental designs for ordered treatments," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    5. 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.

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