Abstract

The purpose of this article is to determine and construct $\varphi$-optimal designs over the class of all circular cross-over designs with two treatments when the number of both periods and experimental subjects is even. We are interested in estimating the contrasts of both direct and carry-over effects jointly, and minimizing the variances of the best linear unbiased estimators of contrasts of direct as well as carry-over effects. These results enrich already existing works in the present literature, strengthening this of Magda (1980), and extending these of Kunert (1984) and Chasiotis and Kounias (2020).

中文翻译：

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两处理循环交叉设计的优化和构建

摘要

本文的目的是确定和构建$\phi$-当两个周期和实验对象的数量是偶数时，在具有两种处理的所有圆形交叉设计类上的最优设计。我们感兴趣的是联合估计直接和结转效应的对比，并最小化直接和结转效应对比的最佳线性无偏估计量的方差。这些结果丰富了现有文献中已有的作品，加强了 Magda (1980) 的作品，并扩展了 Kunert (1984) 和 Chasiotis 和 Kounias (2020) 的作品。