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.

研究并构建了具有异方差误差的回归模型的极小极大稳健设计。这些设计对于模型中的误差方差可能的错误指定具有鲁棒性。我们为误差方差提出了一个灵活的假设，并使用极小极大方法来定义稳健设计。像往常一样，很难通过分析找到稳健的设计，因为相关的设计问题不是凸优化问题。然而，我们可以证明极小极大稳健设计问题的目标函数是两个凸函数的差值。开发了一种有效的算法来计算最小二乘估计和广义最小二乘估计下的极小极大稳健设计。该算法可用于为任何具有异方差误差的线性或非线性回归模型构建极小极大稳健设计。此外，