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.


62K05 Optimal statistical designs
62K10 Statistical block designs
62J99 Linear inference, regression
Full Text: DOI


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