Constrained and compound optimal designs represent two well-known methods for dealing with multiple objectives in optimal design as reflected by two functionals ϕ1 and ϕ2 on the space of information matrices. A constrained optimal design is constructed by optimizing ϕ2 subject to a constraint on ϕ1, and a compound design is found by optimizing a weighted average of the functionals ϕ = λϕ1 + (1 - λ) ϕ2, 0 ≤ λ ≤ 1. We show that these two approaches to handling multiple objectives are equivalent.
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* R. Dennis Cook is Professor, Department of Applied Statistics, University of Minnesota, St. Paul, MN 55 108. Weng Kee Wong is Assistant Professor, Department of Biostatistics, University of California, Los Angeles, CA 90024. The authors thank V. V. Fedorov who provided helpful comments on an earlier version of this work, which was supported in part by National Science Grant DMS-9212413. They also thank the referees and an associate editor who provided useful comments on an earlier version ofthis manuscript.
- D optimality
- Information Matrix
- Large sample design