Extrapolation designs with constraints

The author considers (asymptotically) minimax extrapolation designs for an approximately multiple linear model with the model contaminant f being restricted only by its L₂ norm. He splits the integrated mean squared prediction error (IMSPE) of the fitted value over the extrapolation space into two parts, namely the integrated prediction variance (IPV) and the integrated prediction bias (IPB). For a spherical design space and an annular extrapolation space, he constructs the design that minimizes the maximum value, over f, of IPB subject to bounding IPV. He also constructs the design that minimizes IPV subject to bounding the maximum IPB.