×

zbMATH — the first resource for mathematics

Some optimal designs for comparing a set of test treatments with a set of controls. (English) Zbl 0703.62074
Summary: We give a detailed study of the problem of optimally comparing a set of t test treatments to a set of s controls under a 0-way elimination of heterogeneity model. The relationships between designs that are A and MV- optimal for comparing the test treatments to the controls and those that are A and MV-optimal for comparing all treatments are also studied.

MSC:
62K05 Optimal statistical designs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bechhofer, R. E. and Tamhane, A. C. (1981). Incomplete block designs for comparing treatments with a control; General theory, Technometrics, 23, 45-57. · Zbl 0472.62080
[2] Cheng, C. S., Majumdar, D., Stufken, J. and Ture, T. E. (1988). Optimal step type designs for comparing test treatments with a control, J. Amer. Statist. Assoc., 83, 477-482. · Zbl 0648.62080
[3] Hedayat, A. S. and Majumdar, D. (1984). A-optimal incomplete block designs for control-test treatment comparisons, Technometrics, 26, 360-370. · Zbl 0549.62049
[4] Hedayat, A. S. and Majumdar, D. (1985). A-optimal incomplete block designs for comparing test treatments with a control, Ann. Statist., 13, 757-767. · Zbl 0586.62113
[5] Hedayat, A. S., Jacroux, M. and Majumdar, D. (1988). Optimal designs for comparing test treatments with controls, Statist. Sci., 3, 462-491. · Zbl 0955.62616
[6] Jacroux, M. (1986). On the usage of refined linear models for determining N-way classification designs which are optimal for comparing test treatments with a standard treatment, Ann. Inst. Statist. Math., 38, 569-581. · Zbl 0611.62095
[7] Jacroux, M. (1987a). On the determination and construction of MV-optimal block designs for comparing test treatments with a standard treatment, J. Statist. Plann. Inference, 15, 205-225. · Zbl 0598.62088
[8] Jacroux, M. (1987b). Some MV-optimal block designs for comparing test treatments with a standard treatment. Sankhy? Ser. B, 49, 239-261. · Zbl 0598.62088
[9] Jacroux, M. (1989). On the A-optimality of block designs for comparing test treatment with a control, J. Amer. Statist. Assoc., 84, 310-317. · Zbl 0687.62062
[10] Majumdar, D. (1986). Optimal designs for comparisons between two sets of treatments, J. Statist. Plann. Inference, 14, 359-377. · Zbl 0603.62082
[11] Majumdar, D. and Notz, W. (1983). Optimal incomplete block designs for comparing treatments with a control, Ann. Statist., 11, 258-266. · Zbl 0507.62070
[12] Notz, W. (1985). Optimal designs for treatment-control comparisons in the presence of two-way heterogeneity, J. Statist. Plann. Inference, 12, 61-73. · Zbl 0572.62061
[13] Stufken, J. (1987). A-optimal block designs for comparing test treatments with a control, Ann. Statist., 15, 1629-1638. · Zbl 0629.62077
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.