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D-optimal chemical balance weighing designs with \(N \equiv 0\) (mod 4) and 3 objects. (English) Zbl 1271.62175

Summary: The problem of estimation of the individual weights of three objects using a chemical balance weighing design is considered. We use the criterion of D-optimality. We assume that the covariance matrix of errors is the matrix of a first-order autoregressive process. Such problems were discussed by C.-H. Li and S.-H. Yang [Linear Algebra Appl. 400, 279–290 (2005; Zbl 1140.62336)] and also by H.-G. Yeh and M.-N. L. Huang [Metrika 61, No. 3, 261–275 (2005; Zbl 1079.62078)]. We present some results of D-optimal designs in a certain class of designs with the design matrix \(\mathbf X\in M_{n\times 3}(\pm 1)\) such that each column of the matrix \(\mathbf X\) has at least one 1 and one \(-1\).

MSC:

62K05 Optimal statistical designs
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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References:

[1] DOI: 10.1214/aos/1176345202 · Zbl 0466.62066 · doi:10.1214/aos/1176345202
[2] Horn R. A., Matrix Analysis (1985) · Zbl 0576.15001 · doi:10.1017/CBO9780511810817
[3] DOI: 10.1214/aoms/1177731236 · Zbl 0063.02076 · doi:10.1214/aoms/1177731236
[4] DOI: 10.1016/j.laa.2004.11.020 · Zbl 1140.62336 · doi:10.1016/j.laa.2004.11.020
[5] DOI: 10.1007/s001840400336 · Zbl 1079.62078 · doi:10.1007/s001840400336
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