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Identification of universally optimal circular designs for the interference model. (English) Zbl 1378.62027

The authors consider block designs in an interference model which models not only block and direct treatment effects but also neighbor and edge effects. They investigate in detail so-called circular designs especially wrt their optimality. As usual, they use approximate design theory, especially they look for universally optimal design measures in the sense of J. Kiefer [in: Surv. Stat. Des. Lin. Models, Int. Symp. Fort Collins 1973. 333–353 (1975; Zbl 0313.62057)]. The authors succeed in finding equivalent conditions for any design to be universally optimal for any size of experiment and any covariance structure of the error terms. If the within-block covariance is of so-called type-H (loosely spoken, not far from identity matrix) they present stronger results. As an example, they can show that the circular neighbor balanced designs at distances 1 and 2 (CNBD2) are highly efficient among all possible designs when the error terms are homoscedastic and uncorrelated. However, when the error terms are correlated CNBD2 will be outperformed by other designs. For some theorems, the proofs from an earlier paper are used [Ann. Stat. 43, No. 4, 1596–1616 (2015; Zbl 1331.62383)].

MSC:

62K10 Statistical block designs
62K05 Optimal statistical designs
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