On the equivalence of constrained and compound optimal designs. (English) Zbl 0799.62081

Cook, R. Dennis; Wong, Weng Kee

J. Am. Stat. Assoc. 89, No. 426, 687-692 (1994).

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

Keywords:

D-optimality; efficiency; large sample design; compound optimal designs; space of information matrices; constrained optimal designs; weighted average