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In the present paper we consider design criteria which depend on severaldesigns simultaneously. We formulate equivalence theorems based on momentmatrices (if criteria depend on designs via moment matrices) or with respect tothe designs themselves (for finite design regions). We apply the obtainedoptimality conditions to the multiple-group random coefficient regressionmodels and illustrate the results by simple examples.

Equivalence theorems for compound design problems with application in mixed models