In experimental design it often happens that values of some of the relevant carriers cannot be specified by the experimenter. We consider the problem of obtaining approximate D-optimal designs when the design space is a product space and the carriers associated with one margin are not subject to control. An equivalence theorem for D-optimal designs is presented. The essential ingredients of iterative schemes for generating designs are discussed and an example is presented.
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Cook et al. (1980) studied this question.
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