In the present paper we consider design criteria which depend on several designs simultaneously. We formulate equivalence theorems based on information matrices (if criteria depend on designs via information matrices) or with respect to the designs themselves (for finite design regions). We apply the obtained optimality conditions to multiple-group random coefficient regression models and illustrate the results by simple examples.

中文翻译：

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在混合模型中应用的多重设计问题的等价定理

在本文中，我们考虑同时依赖于多个设计的设计标准。我们根据信息矩阵（如果标准取决于通过信息矩阵的设计）或关于设计本身（对于有限设计区域）来制定等价定理。我们将获得的最优性条件应用于多组随机系数回归模型，并通过简单的例子说明结果。