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Optimal Designs for Proportional Interference Models with Different Guarding Strategies

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  • Futao Zhang

    (Department of Statistics, Beijing Institute of Technology, Beijing 100081, China)

  • Xiangshun Kong

    (Department of Statistics, Beijing Institute of Technology, Beijing 100081, China)

Abstract

Interference models are commonly used in agriculture, industry, and other related fields. Optimal designs for these models are important topics in block designs. In this work, we consider both direct and total effects under both guarded and unguarded proportional interference models. Some general equivalence theorems are established to characterize such efficient designs. For guarded models, we generate optimal noncircular designs for estimating both direct and total effects, respectively. Particularly, we remove the traditional circular assumption for guarded models and introduce noncircular designs which have less restriction and, more importantly, perform higher efficiency than existing circular designs. For unguarded models, we also give the construction of some optimal designs under the proportional interference model.

Suggested Citation

  • Futao Zhang & Xiangshun Kong, 2023. "Optimal Designs for Proportional Interference Models with Different Guarding Strategies," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:443-:d:1035598
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    References listed on IDEAS

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    1. K. Filipiak & A. Markiewicz, 2005. "Optimality and efficiency of circular neighbor balanced designs for correlated observations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(1), pages 17-27, February.
    2. R. A. Bailey & J. Kunert, 2006. "On optimal crossover designs when carryover effects are proportional to direct effects," Biometrika, Biometrika Trust, vol. 93(3), pages 613-625, September.
    3. Norman R. Draper & Irwin Guttman, 1980. "Incorporating Overlap Effects from Neighbouring Units into Response Surface Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(2), pages 128-134, June.
    4. Kunert, Joachim & Martin, R. J., 2000. "On the determination of optimal designs for an interference model," Technical Reports 2000,17, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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