Optimal design measures with singular information matrices

Abstract

SUMMARY The problem of establishing a useful necessary and sufficient condition for a design measure with singular information matrix to be D s -optimal is well known. In this paper a sufficient condition involving a certain type of g -inverse is established for a more general convex criterion function to be minimized by such a design measure. The condition is necessary for D A -optimality and for a linear criterion function. There is some discussion about its necessity in general.