Minimax robust designs for regression models with heteroscedastic errors

Minimax robust designs for regression models with heteroscedastic errors are studied and constructed. These designs are robust against possible misspecification of the error variance in the model. We propose a flexible assumption for the error variance and use a minimax approach to define robust designs. As usual it is hard to find robust designs analytically, since the associated design problem is not a convex optimization problem. However, we can show that the objective function of the minimax robust design problem is a difference of two convex functions. An effective algorithm is developed to compute minimax robust designs under the least squares estimator and generalized least squares estimator. The algorithm can be applied to construct minimax robust designs for any linear or nonlinear regression model with heteroscedastic errors. In addition, several theoretical results are obtained for the minimax robust designs.