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 [xi] be any design on a compact space with a nonsingular information matrix, and let m+[epsilon] be the maximum of the variance function d([xi],x) over all . We prove that any support point x* of a D-optimum design on must satisfy the inequality . 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.