Improvements on removing nonoptimal support points in DD-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 ξξ be any design on a compact space X⊂RmX⊂Rm with a nonsingular information matrix, and let m+εm+ε be the maximum of the variance function d(ξ,x)d(ξ,x) over all x∈Xx∈X. We prove that any support point x*x* of a D  -optimum design on XX must satisfy the inequality d(ξ,x*)⩾m(1+ε/2-ε(4+ε-4/m)/2). We show that this new lower bound on d(ξ,x*)d(ξ,x*) is, in a sense, the best possible, and how it can be used to accelerate algorithms for D-optimum design.