A delimitation of the support of optimal designs for Kiefer’s ϕp-class of criteria

The paper extends the result of Harman and Pronzato [Harman, R., Pronzato, L., 2007. Improvements on removing non-optimal support points in D-optimum design algorithms. Statistics & Probability Letters 77, 90–94], which corresponds to p=0, to all strictly concave criteria in Kiefer’s ϕp-class. We show that, for any given design measure ξ, any support point x∗ of a ϕp-optimal design is such that the directional derivative of ϕp at ξ in the direction of the delta measure at x∗ is larger than some bound hp[ξ] which is easily computed.