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Biometrika 1997 84(2):443-454; doi:10.1093/biomet/84.2.443
© 1997 by Biometrika Trust
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Efficient block designs for setting with spatially correlated errors

NIZAM UDDIN and JOHN P. MORGAN

Department of Mathematics, Tennessee Technological University Cookeville, Tennessee 38505, U.S.A. e-mail: nu3655{at}tntech.edu
Department of Mathematics and Statistics, Old Dominion University Norfolk, Virginia 23529, U.S.A.

Two-dimensional block designs, with block size p x 2 for v treatments, are studied for situations in which the errors are spatially correlated. Conditions for universal optimality are given for two different error covariance structures, the doubly geometric, for which the correlations decay rapidly, and the autonormal, which exhibits a slower rate of decay. In the special cases of p = 1/2v for even v to obtain complete blocks, and p = 1/2(v – 1) for odd v for nearly complete blocks, numerical calculations establish that much smaller designs, using only a fraction of the blocks required by universal optimality, are also reasonably efficient. A table of designs with v ≤30 is included.

Key Words: Autonormal process • Correlated errors • Doubly geometric process • Efficiency • Generalised least squares • Neighbour design • Optimal design


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