Sathe, Y. S.; Shenoy, R. G. Construction method for some A- and D-optimal weighing designs when N\(\equiv 3\,\,(mod\,4)\). (English) Zbl 0731.62131 J. Stat. Plann. Inference 24, No. 3, 369-375 (1990). Summary: Let n and N be positive integers and let \({\mathcal X}(N,n)\) be the set of all \(N\times n\) matrices X whose elements are \(+1\) or -1. If X minimizes \(tr(X'X)^{-1}(\det (X'X)^{-1})\) then X is said to be A-optimal (D- optimal) in \({\mathcal X}(N,n)\). For \(N\equiv 3\) (mod 4), a lower bound for \(tr(X'X)^{-1}(\det (X'X)^{-1})\) has been obtained by the authors [Ann. Stat. 17, No.4, 1906-1915 (1989; Zbl 0695.62190)] and it is shown that this bound is attained if X is such that \(X'X\) is a block matrix with specified blocks of only one size or of two contiguous sizes. In this paper some A- and D-optimal X attaining the lower bound for \(n\leq N-3\) are constructed by deleting s-4 specified rows of a Hadamard matrix of order N-3 and then augmenting it by s-1 specified rows for \(5\leq s\leq 8\). Tables of A- and D-optimal designs thus constructed are given for \(N<100\). Cited in 11 Documents MSC: 62K05 Optimal statistical designs 62K15 Factorial statistical designs 62K10 Statistical block designs 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.) Keywords:weighing designs; A-optimal; block matrix; lower bound; Hadamard matrix; Tables; D-optimal designs Citations:Zbl 0695.62190 PDFBibTeX XMLCite \textit{Y. S. Sathe} and \textit{R. G. Shenoy}, J. Stat. Plann. Inference 24, No. 3, 369--375 (1990; Zbl 0731.62131) Full Text: DOI References: [1] Ehlich, H., Determinantenabschätzungen fur binäre Matrizen mit \(n\)≡3 mod 4, Math. Z., 84, 438-447 (1964) · Zbl 0208.39803 [2] Farmakis, N.; Kounias, S., Two new D-optimal designs (83,56,12), (83,55,12), J. Statist. Plann. Inference, 15, 247-257 (1987) · Zbl 0601.62092 [3] Galil, Z.; Kiefer, J., D-optimum weighing designs, Ann. Statist., 8, 1293-1306 (1980) · Zbl 0466.62066 [4] Galil, Z.; Kiefer, J., Construction methods for D-optimum weighing designs when \(n\)≡3 (mod 4), Ann. Statist., 10, 502-510 (1982) · Zbl 0489.62068 [5] Kounias, S.; Chadjipantelis, T., Some D-optimal weighing designs when \(n\)≡3 (mod 4), J. Statist. Plann. Inference, 8, 117-127 (1983) · Zbl 0519.62059 [6] Kounias, S.; Farmakis, N., A construction of D-optimal weighing designs when \(N\)≡3 (mod 4), J. Statist. Plann. Inference, 10, 177-187 (1984) · Zbl 0561.62067 [7] Sathe, Y. S.; Shenoy, R. G., Optimal values of \(s\) for \(N\)≡3 (mod 4) and \(N<100\) for A-optimal weighing designs (1988), Unpublished manuscript · Zbl 0731.62131 [8] Sathe, Y. S.; Shenoy, R. G., A-optimal weighing designs when \(N\)≡3 (mod 4), Ann. Statist., 17, 4 (1989) · Zbl 0695.62190 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.