Robust optimal extrapolation designs

We study robustness properties of optimal extrapolation designs at a single point under various model assumptions. A curious result is the efficiency of the optimal extrapolation design for a polynomial of degree m is the same whether the true underlying model is a polynomial of degree k or m - k (k = 1, 2,.., m - 1). In addition, the loss in efficiency of the optimal extrapolation designs is between 40-50% when we overestimate the degree of the polynomial model and the extrapolated point is 'far' from the design space. We propose a new class of optimality criteria for extrapolation. The new optimal extrapolation designs are shown to be more efficient and robust to the regression functions. They enjoy good power for discriminating among polynomial models and, if the extrapolated point is sufficiently 'far' from the design space, they coincide with the optimal discrimination designs studied in Dette (1994).