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On the equivalence of constrained and compound optimal designs. (English) Zbl 0799.62081
Summary: Constrained and compound optimal designs represent two well-known methods for dealing with multiple objectives in optimal design as reflected by two functionals \(\varphi_ 1\) and \(\varphi_ 2\) on the space of information matrices. A constrained optimal design is constructed by optimizing \(\varphi_ 2\) subject to a constraint on \(\varphi_ 1\), and a compound design is found by optimizing a weighted average of the functionals \(\varphi = \lambda \varphi_ 1 + (1 - \lambda) \varphi_ 2\), \(0 \leq \lambda \leq 1\). We show that these two approaches to handling multiple objectives are equivalent.

MSC:
62K05 Optimal statistical designs
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