A delimitation of the support of optimal designs for Kiefer’s ϕpϕp-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 DD-optimum design algorithms. Statistics & Probability Letters 77, 90–94], which corresponds to p=0p=0, to all strictly concave criteria in Kiefer’s ϕpϕp-class. We show that, for any given design measure ξξ, any support point x∗ of a ϕpϕp-optimal design is such that the directional derivative of ϕpϕp at ξξ in the direction of the delta measure at x∗ is larger than some bound hp[ξ]hp[ξ] which is easily computed.