Techniques for the construction of robust regression designs

The authors review and extend the literature on robust regression designs. Even for straight line regression, there are cases in which the optimally robust designsin a minimax mean squared error sense, with the maximum evaluated as the true model varies over a neighbourhood of that fitted by the experimenterhave not yet been constructed. They fill this gap in the literature, and in so doing introduce a method of construction that is conceptually and mathematically simpler than the sole competing method. The technique used injects additional insight into the structure of the solutions. In the cases that the optimality criteria employed result in designs that are not invariant under changes in the design space, their methods also allow for an investigation of the resulting changes in the designs. The Canadian Journal of Statistics 41: 679-695; 2013 (c) 2013 Statistical Society of Canada