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A note on D-optimal chemical balance weighing designs with autocorrelated observations

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  • Łukasz Smaga

    (Adam Mickiewicz University)

Abstract

In this paper, D-optimal chemical balance weighing designs with three objects are considered. The error terms are assumed to form a first-order autoregressive process, which implies that the covariance matrix of the vector of errors depends on the known parameter $$\rho $$ ρ . It is shown that the designs constructed by Katulska and Smaga (Metrika 76:393–407, 2013) are still D-optimal weighing designs with three objects under a wider interval of possible values for parameter $$\rho $$ ρ than that considered in that paper. Those designs are also proved to be highly D-efficient designs, when D-optimal design is not known.

Suggested Citation

  • Łukasz Smaga, 2016. "A note on D-optimal chemical balance weighing designs with autocorrelated observations," Statistical Papers, Springer, vol. 57(3), pages 721-730, September.
    • Handle: RePEc:spr:stpapr:v:57:y:2016:i:3:d:10.1007_s00362-015-0676-0
    DOI: 10.1007/s00362-015-0676-0
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    References listed on IDEAS

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    1. Krystyna Katulska & Łukasz Smaga, 2013. "D-optimal chemical balance weighing designs with autoregressive errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(3), pages 393-407, April.
    2. Hong-Gwa Yeh & Mong-Na Lo Huang, 2005. "On exact D-optimal designs with 2 two-level factors and n autocorrelated observations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 261-275, June.
    3. Małgorzata Graczyk, 2009. "Regular A-optimal design matrices X=(x ij ) with x ij =−1, 0, 1," Statistical Papers, Springer, vol. 50(4), pages 789-795, August.
    4. Ceranka, Bronislaw & Graczyk, Malgorzata & Katulska, Krystyna, 2006. "A-optimal chemical balance weighing design with nonhomogeneity of variances of errors," Statistics & Probability Letters, Elsevier, vol. 76(7), pages 653-665, April.
    5. Angelis, L. & Bora-Senta, E. & Moyssiadis, C., 2001. "Optimal exact experimental designs with correlated errors through a simulated annealing algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 37(3), pages 275-296, September.
    Full references (including those not matched with items on IDEAS)

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