# zbMATH — the first resource for mathematics

Optimal regression designs under random block-effects models. (English) Zbl 0828.62066
Summary: $$D$$-optimal regression designs under random block-effects models are considered. In addition to selecting design points, an experimenter also needs to specify how they are grouped into blocks. We first consider minimum-support designs, which are supported on the minimum number of design points. In this case, it is shown that a $$D$$-optimal design can be obtained by combining a $$D$$-optimal block design (for treatment comparisons under random block-effects models) with a $$D$$-optimal regression design under the usual uncorrelated model. Such a design, however, is not optimal when there are no restrictions on the competing designs. To attack the general problem of constructing optimal designs without restrictions on the competing designs, we sketch an approach based on the approximate theory, and apply it to quadratic regression on $$[-1,1]$$.

##### MSC:
 62K05 Optimal statistical designs 62K10 Statistical block designs