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- W2097828776 abstract "In this paper, we consider the estimation problem of individual weights of three objects. For the estimation we use the chemical balance weighing design and the criterion of D-optimality. We assume that the error terms $${varepsilon_{i}, i=1,2,dots,n,}$$ are a first-order autoregressive process. This assumption implies that the covariance matrix of errors depends on the known parameter ρ. We present the chemical balance weighing design matrix $${widetilde{bf X}}$$ and we prove that this design is D-optimal in certain classes of designs for $${rhoin[0,1)}$$ and it is also D-optimal in the class of designs with the design matrix $${{bf X} in M_{ntimes 3}(pm 1)}$$ for some ρ ≥ 0. We prove also the necessary and sufficient conditions under which the design is D-optimal in the class of designs $${M_{ntimes 3}(pm 1)}$$ , if $${rhoin[0,1/(n-2))}$$ . We present also the matrix of the D-optimal factorial design with 3 two-level factors." @default.
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- W2097828776 date "2012-04-19" @default.
- W2097828776 modified "2023-10-18" @default.
- W2097828776 title "D-optimal chemical balance weighing designs with autoregressive errors" @default.
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- W2097828776 doi "https://doi.org/10.1007/s00184-012-0394-8" @default.
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