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D -Optimal Designs for Binary and Weighted Linear Regression Models: One Design Variable

Author

Listed:
  • Necla Gündüz

    (Department of Statistics, University of Gazi, Ankara 06560, Turkey)

  • Bernard Torsney

    (School of Mathematics & Statistics, University of Glasgow, Glasgow G12 8QQ, Scotland, UK)

Abstract

D -optimality is a well-known concept in experimental design that seeks to select an optimal set of design points to estimate the unknown parameters of a statistical model with a minimum variance. In this paper, we focus on proving a conjecture made by Ford, Torsney and Wu regarding the existence of a class of D -optimal designs for binary and weighted linear regression models. Our concentration is on models with one design variable. The conjecture states that, for any given level of precision, there exists a two-level factorial design that is D -optimal for these models. To prove this conjecture, we use an intuitive approach that explores various link functions in the generalised linear model context to establish the veracity of the conjecture. We also present explicit and clear plots of various functions wherever deemed necessary and appropriate to further strengthen the proofs. Our results establish the existence of D -optimal designs for binary and weighted linear regression models with one design variable, which have important implications for the efficient design of experiments in various fields. These findings contribute to the development of optimal experimental designs for studying binary and weighted linear regression models and provide a foundation for future research in this area.

Suggested Citation

  • Necla Gündüz & Bernard Torsney, 2023. "D -Optimal Designs for Binary and Weighted Linear Regression Models: One Design Variable," Mathematics, MDPI, vol. 11(9), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2075-:d:1134660
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    References listed on IDEAS

    as
    1. Osama Idais, 2021. "On local optimality of vertex type designs in generalized linear models," Statistical Papers, Springer, vol. 62(4), pages 1871-1898, August.
    2. Habib Jafari & Soliman Khazai & Yazdan Khaki & Tohid Jafari, 2014. "D-Optimal Design for Logistic Regression Model with Three Independent Variables," Journal of Asian Scientific Research, Asian Economic and Social Society, vol. 4(3), pages 120-124, March.
    3. Habib Jafari & Soliman Khazai & Yazdan Khaki & Tohid Jafari, 2014. "D-Optimal Design for Logistic Regression Model with Three Independent Variables," Journal of Asian Scientific Research, Asian Economic and Social Society, vol. 4(3), pages 120-124.
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