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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.

##### MSC:
 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
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##### References:
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