Minimax Designs for the Stability of Slope Estimation on Second-order Response Surfaces

In this paper, designs for the stability of the slope estimation on a second-order response surface are considered. Minimization of the point dispersion measure, which is maximized over all points in the region of interest is taken as the optimality criterion, and the minimax properties in some class of designs are derived in spherical and cubic regions of interest. We study the efficiencies of the minimax designs relative to other optimal designs with various criteria.