Improvements on removing nonoptimal support points in D-optimum design algorithms

We improve the inequality used in Pronzato [2003. Removing non-optimal support points in D-optimum design algorithms. Statist. Probab. Lett. 63, 223-228] to remove points from the design space during the search for a D-optimum design. Let be any design on a compact space X subset of R-m with a nonsingular information matrix, and let m + epsilon be the maximum of the variance function d(xi, x) over all x is an element of X. We prove that any support point x(*) of a D-optimum design on X must satisfy the inequality d(xi, x(*)) >= m(1 + epsilon/2 - root epsilon(4 + epsilon - 4/m)/2). We show that this new lower bound on d(xi, x(*)) is, in a sense, the best possible, and how it can be used to accelerate algorithms for D-optimum design. (c) 2006 Elsevier B.V. All rights reserved.