标准准则和复合准则下最优设计的稳健性比较
Comparing robustness properties of optimal designs under standard and compound criteria
摘要：
标准最优性准则（例如A-、D-最优性准则等）通常用于获得最佳设计。对于给定的统计模型，标准准则假设误差方差在设计阶段已知。然而，在实践中，估计误差方差来推断模型参数。修正准则被定义为标准准则和相应的误差自由度的函数，这可能导致极端的最优设计。复合准则被定义为不同的修改准则和相应的用户指定的权重的函数。对于$3^3$析因设计，得到了基于标准、修正和复合准则的最优设计。最优设计的鲁棒性进行了比较。
英文摘要：
Standard optimality criteria (e.g. A-, D-optimality criterion, etc.) have been commonly used for obtaining optimal designs. For a given statistical model, standard criteria assume the error variance is known at the design stage. However, in practice the error variance is estimated to make inference about the model parameters. Modified criteria are defined as a function of the standard criteria and the corresponding error degrees of freedom, which may lead to extreme optimal design. Compound criteria are defined as the function of different modified criteria and corresponding user specified weights. Standard, modified, and compound criteria based optimal designs are obtained for $3^3$ factorial design. Robustness properties of the optimal designs are also compared.
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