Construction of optimal designs in random coefficient regression models

Abstract

We consider the problem of optimal experimental design in random coefficient regression models with respect to a quadratic loss function. By application of WHITTLE'S general equivalence theorem we obtain the structure of optimal designs. An alogrithm is given which allows, under certain assumptions, the construction of the information matrix of an optimal design. Moreover, we give conditions on the equivalence of optimal designs with respect to optimality criteria which are analogous to usual A-D- and _E/-optimality.

Keywords:

• Bayesian linear models
• Linear BAYES estimator
• Information matrix
• Experimental design
• Structure of optimal designs
• Equivalence theorems