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Biometrika 1987 74(4):717-724; doi:10.1093/biomet/74.4.717
© 1987 by Biometrika Trust
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Neighbour balanced block designs for correlated errors

JOACHIM KUNERT

Fachbereich IV-Mathematik/Statistik, Universität Trier D-5500 Trier, Federal Republic of Germany

The paper considers a simple block model and assumes that the errors within the blocks are correlated, following a stationary first-order autoregressive process. Gill & Shukla (1985) consider this model, but they restrict the set of the competing designs to a small subset of the possible designs, the binary and equireplicate designs. In the present paper we show that the designs determined by Gill & Shukla are optimal over all possible designs for positive correlations and that neighbour balanced designs in general are highly efficient.

Key Words: Block design • Correlated errors • Efficient design • Neighbour balance • Universal optimality • Weighted least-squares


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