zbMATH — the first resource for mathematics

A note on optimal designs with a non-orthogonal row-column-structure. (English) Zbl 0786.62075
Summary: Recently, there has been a number of papers on designs with a non- orthogonal row-column structure. A common feature of the optimal designs derived in those papers was that they tried to balance the number of appearances of the treatments in the rows and in the columns as well as possible. The present note shows that in the case of a non-orthogonal row-column structure this is not always a good strategy for the search for optimal designs. As an example, we give a series of optimal designs for a certain non-orthogonal row-column structure which are not always optimal if there are only column effects but no row effects in the model.

62K05 Optimal statistical designs
62K10 Statistical block designs
Full Text: DOI
[1] Baksalary, J.K.; Pukelsheim, F.; Schach, S.; Trenkler, G., Adjusted orthogonality properties in multiway block designs, Data analysis and statistical inference, Festschrift in honour of friedhelm eicker. eul verlag, Köln, 413-420, (1992) · Zbl 0786.62077
[2] Jacroux, M.; Saharay, R., On the determination and construction of optimal row—column designs having unequal row and column sizes, Ann. inst. statist. math., 43, 377-390, (1991) · Zbl 0761.62104
[3] Kiefer, J., Construction and optimality of generalized youden designs, (), 333-353 · Zbl 0313.62057
[4] Kunert, J., Optimal design and refinement of the linear model with application to repeated measurements designs, Ann. stat., 11, 247-257, (1983) · Zbl 0522.62054
[5] Kurotschka, V., Optimal design of complex experiments with qualitative factors of influence, Comm. stat.—theor. meth., A7, 1363-1378, (1978) · Zbl 0392.62057
[6] Mukhopadhyay, A.C.; Saharay, R., Three way elimination of heterogeneity with non-orthogonal incidence structure for every two directions, Sankhyā B, 50, 181-194, (1978) · Zbl 0654.62063
[7] Saharay, R., Optimal designs under a certain class of non-orthogonal row—column structure, Sankhyā B, 48, 44-67, (1986)
[8] Shah, K.R.; Sinha, B.K., Workshop on Linear Models, Experimental Designs, and Related Matrix Theory in Tampere, Finland, August 6-8, 1990, Optimality aspects of row—column designs with non-orthogonal structure, (1990), Paper presented at the
[9] Steward, F.P.; Bradley, R.A., Some universally optimal row—column designs with empty nodes, Biometrika, 78, 337-348, (1991) · Zbl 0735.62072
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.