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Schur- and E-optimal two-level factorial designs

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  • Butler, Neil A.

Abstract

Schur-optimality is a very general class of optimality criteria that includes, as special cases, A- D- and E-optimality and Cheng Type 1 optimality. In this paper, Schur-optimal two-level factorial designs under a second-order model are derived for 3 and 5 factors for all numbers of runs where the model is estimable. In addition, orthogonal arrays of strength 4 (resolution V) with e added runs are shown to be E-optimal under a second-order model for e[less-than-or-equals, slant]10 and m=4 factors and for e[less-than-or-equals, slant]15 and m[greater-or-equal, slanted]5 factors. Corresponding results for third-order models are also given.

Suggested Citation

  • Butler, Neil A., 2008. "Schur- and E-optimal two-level factorial designs," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 518-527, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:5:p:518-527
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    References listed on IDEAS

    as
    1. Neil A. Butler & Victorino M. Ramos, 2007. "Optimal additions to and deletions from two‐level orthogonal arrays," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 51-61, February.
    2. Neil A. Butler, 2006. "Optimal blocking of two-level factorial designs," Biometrika, Biometrika Trust, vol. 93(2), pages 289-302, June.
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