Optimality and bias of some interpolation and extrapolation designs

We consider interpolation and extrapolation designs with controlled bias. A consistent estimate of an upper bound of the bias is presented. The estimate of some extrapolated value is obtained in a two-stage procedure. The first one provides an estimate of some interpolated value. The second one uses a Taylor expansion around this point. This procedure yields a new type of designs. We discuss their optimality properties with respect to the variance and the bias.