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Optimality of neighbour balanced designs. (English) Zbl 0939.62076
Summary: The purpose of this paper is to study optimality of circular neighbour-balanced block designs when neighbour effects are present in the model. Universal optimality of these designs is shown for treatment and neighbour effects over a large class of competing designs. We bring special attention to designs with \(t-1\) blocks of length \(t\) and designs with \(t\) blocks of length \(t-1\), where \(t\) is the number of treatments. In order to establish the optimality, we use J. Kiefer’s results in Surv. Stat. Des. Lin. Models, Int. Symp. Fort Collins 1973, 333-353 (1975; Zbl 0313.62057), avoiding the calculation of generalised inverses. Then, we give some examples where circular neighbour-balanced block designs are no longer optimal.

62K05 Optimal statistical designs
62K10 Statistical block designs
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text: DOI
[1] Azaı̈s, J.-M.; Bailey, R.A.; Monod, H., A catalogue of efficient neighbour-designs with border plots, Biometrics, 49, 1252-1261, (1993)
[2] Azaı̈s, J.-M.; Druilhet, P., Optimality of neighbour-balanced designs when neighbour effects are neglected, J. statist. plann. inference, 64, 353-367, (1997) · Zbl 0908.62074
[3] Bermond, J.-C.; Faber, V., Decomposition of the complete directed graph into k-circuits. J. combin. theory B, 21, 145-155, (1976) · Zbl 0344.05123
[4] Cheng, C.-S.; Wu, C.F., Balanced repeated measurements designs, Ann. statist., 8, 1272-1283, (1980) · Zbl 0461.62064
[5] Cheng, C.-S.; Wu, C.F., Correction to: balanced repeated measurements designs, Ann. statist., 11, 349, (1983) · Zbl 0518.62061
[6] Collombier, D.; Merchermek, I., Optimal cross-over experimental designs, Sankhyā B, 55, 249-261, (1993) · Zbl 0803.62064
[7] Hedayat, A.; Afsarinejad, K., Repeated measurements designs, Ann. statist., 6, 619-628, (1978) · Zbl 0395.62056
[8] Kiefer, J., 1975. Construction and optimality of generalized youden designs. In: A Survey of Statistical Design and Linear Models. North-Holland, Amsterdam, pp. 333-353.
[9] Kunert, J., Optimal design and refinement of the linear model with applications to repeated measurements designs, Ann. statist., 11, 247-257, (1983) · Zbl 0522.62054
[10] Kunert, J., Designs balanced for circular residual effects, Comm. statist. theory meth. A, 13, 2665-2671, (1984) · Zbl 0565.62048
[11] Kunert, J., Optimality of balanced uniform repeated measurements designs, Ann. statist., 12, 1006-1017, (1984) · Zbl 0544.62068
[12] Langton, S., Avoiding edge effects in agroforestry experiments; the use of neighbour-balanced designs and guard areas, Agroforestry systems, 12, 173-185, (1990)
[13] Magda, C.G., Circular balanced repeated measurements designs, Comm. statist. theory meth. A, 9, 1901-1918, (1980) · Zbl 0457.62061
[14] Mahfouz, M., 1988. Plans d’expériences optimaux et compétition entre traitements. Thèse de 3^e cycle, Université de Pau et des pays de l’Adour.
[15] Monod, H., 1991. Construction et randomisation de plans factoriels équilibrés pour les voisinages. Thèse de Doctorat, Institut National Agronomique: Paris-Grignon.
[16] Monod, H.; Bailey, R.A., Valid restricted randomization for unbalanced designs, J. roy. statist. soc. B, 55, 237-251, (1993) · Zbl 0782.62074
[17] Shah, K.R., Sinha, B.K., 1989. Theory of Optimal Designs. Springer, Berlin. · Zbl 0688.62043
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