Katulska, Krystyna; Smaga, Łukasz D-optimal chemical balance weighing designs with \(N \equiv 0\) (mod 4) and 3 objects. (English) Zbl 1271.62175 Commun. Stat., Theory Methods 41, No. 13-14, 2445-2455 (2012). 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 \(-1\). Cited in 4 Documents MSC: 62K05 Optimal statistical designs 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) Keywords:D-optimality; first-order autoregressive processes Citations:Zbl 1140.62336; Zbl 1079.62078 PDFBibTeX XMLCite \textit{K. Katulska} and \textit{Ł. Smaga}, Commun. Stat., Theory Methods 41, No. 13--14, 2445--2455 (2012; Zbl 1271.62175) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.