Abstract Blocking is often used to reduce known variability in designed experiments by collecting together homogeneous experimental units. A common modeling assumption for such experiments is that responses from units within a block are dependent. Accounting for such dependencies in both the design of the experiment and the modeling of the resulting data when the response is not normally distributed can be challenging, particularly in terms of the computation required to find an optimal design. The application of copulas and marginal modeling provides a computationally efficient approach for estimating population‐average treatment effects. Motivated by an experiment from materials testing, we develop and demonstrate designs with blocks of size two using copula models. Such designs are also important in applications ranging from microarray experiments to experiments on human eyes or limbs with naturally occurring blocks of size two. We present a methodology for design selection, make comparisons to existing approaches in the literature, and assess the robustness of the designs to modeling assumptions.

中文翻译：

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基于 Copula 的鲁棒最优块设计

摘要 区组通常用于通过将同质实验单元收集在一起来减少设计实验中已知的变异性。此类实验的常见建模假设是块内单元的响应是相关的。当响应不呈正态分布时，在实验设计和结果数据建模中考虑这种依赖性可能具有挑战性，特别是在寻找最佳设计所需的计算方面。联结和边际建模的应用为估计人群平均治疗效果提供了一种计算有效的方法。受材料测试实验的启发，我们使用 copula 模型开发并演示了尺寸为 2 的块的设计。这种设计在从微阵列实验到利用天然存在的二号块对人眼或四肢进行的实验等应用中也很重要。我们提出了一种设计选择方法，与文献中的现有方法进行比较，并评估设计对建模假设的稳健性。