On the Equivalence of Constrained and Compound Optimal Designs

Abstract

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.

Key Words:

• D optimality
• Efficiency
• Information Matrix
• Large sample design