Robust extrapolation designs for biased polynomial models

Abstract

Abstract In this article we consider the construction of optimal designs for extrapolation in the polynomial regression setup, allowing for imprecision in the specification of the response function. We adopt a minimax approach, which determines an optimal design to minimize the maximum value of the integrated mean-squared prediction error (IMSPE), with the maximum being evaluated over the departures from the model. It turns out that in straight-line and quadratic regression, the minimax extrapolation designs are the same as the minimum integrated variance (MIV) extrapolation designs, which assume that the fitted models are correct. These designs coincide with the D 1 -optimal designs if the extrapolation interval becomes sufficiently large. For cubic polynomial regression, some comparisons of the performance of the proposed designs with uniform and MIV designs are given.