存在模型污染时的最优响应曲面设计
Optimal response surface designs in the presence of model contamination
AI总结：
本研究针对响应曲面实验中模型依赖风险与多目标冲突问题，提出含三类准则的复合最优性框架，适配受限随机化场景，用点交换算法求近似最优设计，通过示例验证权衡效果并给出实用建议。
摘要：
在响应曲面实验中完全依赖拟合模型存在风险，而放宽这一假设——无论是出于必要还是有意为之——都需要实验者权衡多个相互冲突的目标。本研究提出了一个复合最优性准则的方法框架，该框架由多个基本准则组成，分别负责：(i) 基于置信区间、使用拟合模型开展推断的质量（DP-/LP-最优性）；(ii) 提升检验由额外多项式项形式的特定潜在模型污染导致的失拟的能力；(iii) 同时最小化由该模型误设引起的拟合模型参数的方差和偏差。后两个组成部分是依据用于误差估计的、与模型无关的“纯误差”方法新开发的。复合准则与设计构建已适配受限随机化框架：区组实验和多层实验，其中采用了逐层分析的方法。研究使用点交换算法来搜索近似最优设计。在理论工作之外，还通过一个真实案例和两个说明性示例，探究了各组成部分与最优设计特征之间的关联模式，展示了在各竞争目标间可实现的权衡，并提出了一些通用的实用建议。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
