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Optimal regression designs in the presence of random block effects. (English) Zbl 0930.62073

Summary: A- and D-optimal regression designs under random block - effects models are considered. We first identify certain situations where D- and A-optimal designs do not depend on the intra-block correlation and can be obtained easily from the optimal designs under uncorrelated models. For example, for quadratic regression on \([-1,1]\), this covers D-optimal designs when the block size is a multiple of 3 and A-optimal designs when the block size is a multiple of 4.
In general, the optimal designs depend on the intra-block correlation. For quadratic regression, we provide expressions for D-optimal designs for any block size. A-optimal designs with blocks of size 2 for quadratic regression are also obtained. In all the cases considered, robust designs which do not depend on the intrablock correlation can be constructed.

MSC:

62K05 Optimal statistical designs
62K10 Statistical block designs
62J99 Linear inference, regression
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References:

[3] Cheng, C. S., Optimal regression designs under random block effects models, Statist. Sinica, 5, 485-497 (1995) · Zbl 0828.62066
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