论文标题
通过其他因素的计划正交最优性的方面
Aspects of optimality of plans orthogonal through other factors
论文作者
论文摘要
Bagchi（2010）中定义的通过区块因子（OTB）的正交性的概念通过其他因素（例如S）扩展到正交性。我们讨论了这种正交性对估计精确度以及推理程序的影响。当$ s $是二大的情况下，我们专注于案例，我们构建了一系列计划，每对其他因素都是通过给定的因素正交的。 接下来，我们专注于通过块因子（POTB）的计划。我们为具有两个和三级因素的对称实验构建了POTBS。两个因素的计划是极端的，而三级因素的计划是普遍最佳的。 最后，我们为$ s^t（s+1）$实验构造了POTB，其中$ s \ equiv 3 \ pmod 4 $是主要功率。该计划是普遍最佳的。
The concept of orthogonality through the block factor (OTB), defined in Bagchi (2010), is extended here to orthogonality through a set (say S) of other factors. We discuss the impact of such an orthogonality on the precision of the estimates as well as on the inference procedure. Concentrating on the case when $S$ is of size two, we construct a series of plans in each of which every pair of other factors is orthogonal through a given pair of factors. Next we concentrate on plans through the block factors (POTB). We construct POTBs for symmetrical experiments with two and three-level factors. The plans for two factors are E-optimal, while those for three-level factors are universally optimal. Finally, we construct POTBs for $s^t(s+1)$ experiments, where $s \equiv 3 \pmod 4$ is a prime power. The plan is universally optimal.
