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Universally optimal designs under mixed interference models with and without block effects

Author

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  • Katarzyna Filipiak

    (Poznań University of Technology)

  • Augustyn Markiewicz

    (Poznań University of Life Sciences)

Abstract

The literature on neighbor designs as introduced by Rees (Biometrics 23:779–791, 1967) is mainly devoted to construction methods, providing few results on their statistical properties, such as efficiency and optimality. A review of the available literature, with special emphasis on the optimality of neighbor designs under various fixed effects interference models, is given in Filipiak and Markiewicz (Commun Stat Theory Methods 46:1127–1143, 2017). The aim of this paper is to verify whether the designs presented by Filipiak and Markiewicz (2017) as universally optimal under fixed interference models are still universally optimal under models with random interference effects. Moreover, it is shown that for a specified covariance matrix of random interference effects, a universally optimal design under mixed interference models with block effects is universally optimal over a wider class of designs. In this paper the method presented by Filipiak and Markiewicz (Metrika 65:369–386, 2007) is extended and then applied to mixed interference models without or with block effects.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:6:d:10.1007_s00184-017-0628-x
    DOI: 10.1007/s00184-017-0628-x
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    References listed on IDEAS

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    1. Filipiak, K. & Markiewicz, A., 2003. "Optimality of neighbor balanced designs under mixed effects model," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 225-234, February.
    2. Adrian Wilk & Joachim Kunert, 2015. "Optimal crossover designs in a model with self and mixed carryover effects with correlated errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(2), pages 161-174, February.
    3. Katarzyna Filipiak & Augustyn Markiewicz, 2014. "On the Optimality of Circular Block Designs Under a Mixed Interference Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(21), pages 4534-4545, November.
    4. Katarzyna Filipiak & Augustyn Markiewicz, 2017. "Universally optimal designs under interference models with and without block effects," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1127-1143, February.
    5. 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.
    6. 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.
    7. 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.
    8. Filipiak, K. & Markiewicz, A., 2004. "Optimality of type I orthogonal arrays for general interference model with correlated observations," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 259-265, July.
    9. Filipiak, Katarzyna & Rózanski, Rafal & Sawikowska, Aneta & Wojtera-Tyrakowska, Dominika, 2008. "On the E-optimality of complete designs under an interference model," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2470-2477, October.
    10. 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.
    11. V. Sharma, 2013. "Universally optimal balanced changeover designs with first residuals," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 339-346, April.
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    Cited by:

    1. 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.

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