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On the E-optimality of complete designs under an interference model

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  • Filipiak, Katarzyna
  • Rózanski, Rafal
  • Sawikowska, Aneta
  • Wojtera-Tyrakowska, Dominika

Abstract

In the experiments in which the response to a treatment can be affected by other treatments, the interference model with neighbor effects is usually applied. It is known, that circular neighbor balanced designs (CNBDs) are universally optimal under this model. However, such designs cannot exist for each combination of design parameters. If in the class of block designs with a given number of blocks there exists CNBD, then such a design cannot exist in the class with one block less or more. The aim of this paper is to identify the E-optimal complete block designs under the interference model with neighbor effects over such classes of designs. The results are based on algebraic properties of the information matrix.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2470-2477
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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. Srivastav, Sudesh K. & Shankar, Arti, 2003. "On the E-optimality of certain class of block designs," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 187-193, November.
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    Cited by:

    1. 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.
    2. Katarzyna Filipiak & Razieh Khodsiani & Augustyn Markiewicz, 2019. "Optimality of block designs under the model with the first-order circular autoregression," Statistical Papers, Springer, vol. 60(2), pages 427-447, April.
    3. Katarzyna Filipiak & Rafał Różański, 2009. "Connectedness of complete block designs under an interference model," Statistical Papers, Springer, vol. 50(4), pages 779-787, August.
    4. 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.

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