This paper studies optimal designs for linear regression models with correlated effects for single responses. We introduce the concept of rhombic design to reduce the computational complexity and find a semi-algebraic description for the D-optimality of a rhombic design via the Kiefer-Wolfowitz equivalence theorem. Subsequently, we show that the structure of an optimal rhombic design depends directly on the correlation structure of the random coefficients.

中文翻译：

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具有相关随机系数的多元线性回归模型中设计的最优区域

本文研究了对单个响应具有相关效应的线性回归模型的最佳设计。我们引入了菱形设计的概念来降低计算复杂度，并通过 Kiefer-Wolfowitz 等价定理找到菱形设计的 D 最优性的半代数描述。随后，我们表明最佳菱形设计的结构直接取决于随机系数的相关结构。