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Optimality aspects of row-column designs with non-orthogonal structure. (English) Zbl 0778.62066
Summary: This paper deals with row-column designs in which the row-column incidence patterns are not necessarily orthogonal. A set of sufficient conditions is obtained for universally optimal designs (for comparing treatment effects) to exist in the usual fixed effects 3-factor additive model. It is shown that if these conditions on the row-column incidence pattern are satisfied, a design can always be constructed. Some methods of construction are given for specific row-column incidence patterns. Various other related issues are also discussed.

MSC:
62K05 Optimal statistical designs
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[1] Baranyai, Z., On the factorization of the complete uniform hypergraph, (), 91-108
[2] Cheng, C.S., On the E-optimality of some block designs, J.R. statist. soc. B, 42, 199-204, (1980) · Zbl 0433.62047
[3] Cheng, C.S., Optimality and construction of pseudo-youden designs, Ann. statist., 9, 200-205, (1981) · Zbl 0457.62057
[4] Constantine, G.M., Some E-optimal block designs, Ann. statist., 9, 886-892, (1981) · Zbl 0471.62078
[5] Eccleston, J.A.; Kiefer, J., Relationships of optimality for individual factors of a design, J. statist. plann. inference, 5, 213-219, (1981) · Zbl 0481.62059
[6] Ehrenfeld, S., On the efficiency of experimental designs, Ann. math. statist., 26, 247-255, (1955) · Zbl 0064.38505
[7] Hedayat, A.S.; Afsarinejad, K., Repeated measurements designs I, (), 229-242 · Zbl 0304.62009
[8] Hedayat, A.S.; Afsarinejad, K., Repeated measurements designs II, Ann. statist., 6, 619-628, (1978) · Zbl 0395.62056
[9] Jacroux, M., On the E-optimality of regular graph designs, J. royal statist. soc. ser. B, 42, 205-209, (1980) · Zbl 0443.62063
[10] Katona, G., On separating systems of a finite set, J. comb. theory A, 1, 174-194, (1966) · Zbl 0144.00501
[11] Kiefer, J., On the nonrandomized optimality and randomized nonoptimality of symmetrical designs, Ann. math. statist., 29, 675-699, (1958) · Zbl 0092.36102
[12] Kiefer, J., Optimum experimental designs, J. royal statist. soc. ser. B, 21, 272-319, (1959) · Zbl 0108.15303
[13] Kiefer, J., The role of symmetry and approximation in exact design optimality, (), 109-118 · Zbl 0305.62052
[14] Kiefer, J., Construction and optimality of generalized youden designs, (), 333-353 · Zbl 0313.62057
[15] Kunert, J., Optimality of balanced uniform repeated measurements designs, Ann. statist., 12, 1006-1017, (1984) · Zbl 0544.62068
[16] Kurotschka, V., Optimal design of complex experiments with qualitative factors of influence, Comm. stat. — theor. meth., A7, 1363-1378, (1978) · Zbl 0392.62057
[17] Nandi, H.K., On the efficiency of experimental designs, Cal. stat. assoc. bull., 3, 161-171, (1950)
[18] Pukelsheim, F., Approximate theory of multiway block designs, Canad. J. statist., 14, 339-346, (1986) · Zbl 0621.62081
[19] Ryser, H.J., Combinatorial mathematics, (1963), Wiley New York · Zbl 0112.24806
[20] Saharay, R., Optimal designs under a certain class of non-orthogonal row-column structure, Sankhyā B, 48, 44-67, (1986)
[21] Shah, K.R.; Sinha, B.K., Theory of optimal designs, () · Zbl 0691.62067
[22] Steward, F.P.; Bradley, R.A., Some universally optimal row-column designs with empty nodes, Biometrika, 78, 337-348, (1991) · Zbl 0735.62072
[23] Wald, A., On the efficient design of statistical investigations, Ann. math. statist., 14, 134-140, (1943) · Zbl 0060.30109
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