论文标题
在存在模型污染的情况下，最佳响应表面设计
Optimal response surface designs in the presence of model contamination
论文作者
论文摘要
完全依赖响应表面实验中拟合模型的模型是有风险的，放松了这一假设，无论是出于必要还是故意，都要求实验者考虑多个相互冲突的目标。这项工作提供了一个方法学框架的复合最优标准，该标准包括：（i）使用拟合模型（DP-/LP-Optimality）进行基于置信区域的推断的质量； （ii）以额外的多项式术语的形式提高从指定潜在模型污染中测试缺乏拟合的能力； （iii）同时最小化该错误指定的拟合模型参数的方差和偏差。后两个组件是根据与误差估计的模型无关的“纯错误”方法新开发的。复合标准和设计构建适用于受限制的随机化框架：被阻断和多术实验，其中采用了层面的方法。使用点交换算法来搜索几乎最佳的设计。理论工作伴随着一个真实和两个说明性示例，以探索最佳设计的各个组成部分和特征之间的关系模式，证明了在竞争目标中的可实现折衷，并提出了一些一般的实际建议。
Complete reliance on the fitted model in response surface experiments is risky and relaxing this assumption, whether out of necessity or intentionally, requires an experimenter to account for multiple conflicting objectives. This work provides a methodological framework of a compound optimality criterion comprising elementary criteria responsible for: (i) the quality of the confidence region-based inference to be done using the fitted model (DP-/LP-optimality); (ii) improving the ability to test for the lack-of-fit from specified potential model contamination in the form of extra polynomial terms; and (iii) simultaneous minimisation of the variance and bias of the fitted model parameters arising from this misspecification. The latter two components have been newly developed in accordance with the model-independent 'pure error' approach to the error estimation. The compound criteria and design construction were adapted to restricted randomisation frameworks: blocked and multistratum experiments, where the stratum-by-stratum approach was adopted. A point-exchange algorithm was employed for searching for nearly optimal designs. The theoretical work is accompanied by one real and two illustrative examples to explore the relationship patterns among the individual components and characteristics of the optimal designs, demonstrating the attainable compromises across the competing objectives and driving some general practical recommendations.
