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Circuits for robust designs

Author

Listed:
  • Roberto Fontana

    (Politecnico di Torino)

  • Fabio Rapallo

    (Università di Genova)

  • Henry P. Wynn

    (London School of Economics)

Abstract

This paper continues the application of circuit theory to experimental design started by the first two authors. The theory gives a very special and detailed representation of the kernel of the design model matrix named circuit basis. This representation turns out to be an appropriate way to study the optimality criteria referred to as robustness: the sensitivity of the design to the removal of design points. Exploiting the combinatorial properties of the circuit basis, we show that high values of robustness are obtained by avoiding small circuits. Many examples are given, from classical combinatorial designs to two-level factorial designs including interactions. The complexity of the circuit representations is useful because the large range of options they offer, but conversely requires the use of dedicated software. Suggestions for speed improvement are made.

Suggested Citation

  • Roberto Fontana & Fabio Rapallo & Henry P. Wynn, 2022. "Circuits for robust designs," Statistical Papers, Springer, vol. 63(5), pages 1537-1560, October.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:5:d:10.1007_s00362-021-01285-6
    DOI: 10.1007/s00362-021-01285-6
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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. Roberto Fontana & Fabio Rapallo, 2019. "On the aberrations of mixed level orthogonal arrays with removed runs," Statistical Papers, Springer, vol. 60(2), pages 479-493, April.
    3. Radoslav Harman & Lenka Filová & Peter Richtárik, 2020. "A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 348-361, January.
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    Citations

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    Cited by:

    1. Elena Pesce & Fabio Rapallo & Eva Riccomagno & Henry P. Wynn, 2023. "Generation of all randomizations using circuits," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(4), pages 683-704, August.

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