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Universally optimal balanced block designs for interference model

Author

Listed:
  • Akram Fakhari-Esferizi

    (Isfahan University of Technology)

  • Saeid Pooladsaz

    (Isfahan University of Technology)

Abstract

The interference model has been widely used and studied in block designs where the treatment in a particular plot effects on ones in its neighbor plots. There are many experiments specially in agricultre that block size (k) is greater than the number of treatment (t). If $$k>t$$ k > t , the universally optimal designs under the interference models are usually difficult to obtain. In this paper, we consider an interference model with equal left- and right-neighbor effects for uncorrelated errors when $$k>t$$ k > t . Based on Kushner’s method, we obtain the universally optimal designs on the class of circular block designs. We also present some methods to construct these designs. Then, we generalize our results for one-sided interference models.

Suggested Citation

  • Akram Fakhari-Esferizi & Saeid Pooladsaz, 2022. "Universally optimal balanced block designs for interference model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(8), pages 1049-1061, November.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:8:d:10.1007_s00184-022-00870-5
    DOI: 10.1007/s00184-022-00870-5
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    References listed on IDEAS

    as
    1. S. Pooladsaz & R. J. Martin, 2005. "Optimal extended complete block designs for dependent observations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 185-197, April.
    2. K. Filipiak & A. Markiewicz, 2007. "Optimal designs for a mixed interference model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(3), pages 369-386, May.
    3. Katarzyna Filipiak & Augustyn Markiewicz, 2017. "Universally optimal designs under mixed interference models with and without block effects," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 789-804, November.
    4. 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.
    5. Filipiak, Katarzyna, 2012. "Universally optimal designs under an interference model with equal left- and right-neighbor effects," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 592-598.
    6. Khodsiani, R. & Pooladsaz, S., 2017. "Universal optimal block designs under hub correlation structure," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 387-392.
    7. 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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