Equivalence Theorems and Cutting Plane Algorithms for a Class of Experimental Design Problems

Abstract

Optimum experimental design seeks to allocate measurement resources in regression problems so that best linear estimators of unknown parameters are optimal with respect to some function of their covariance matrices. An equivalence theorem is given for a class of design problems including minimizing the determinant of some specified minor of the covariance matrix, or minimizing its trace. The main theorem gives a system of linear inequalities whose solution set is the set of optimal information matrices, including those singular matrices which are optimal in the limit. This approach yields cutting-plane methods which permit intermediate designs to have singular information matrices.