Identification of universally optimal circular designs for the interference model
研究了循环设计在干扰模型下的最优性，发现距离1和2的循环邻域平衡设计（CNBD2）在误差项同方差且不相关时高效，但误差相关时表现不佳；提出了任意设计通用最优的等价条件，适用于任何实验规模和误差协方差结构。
Many applications of block designs exhibit neighbor and edge effects. A popular remedy is to use the circular design coupled with the interference model. The search for optimal or efficient designs has been intensively studied in recent years. The circular neighbor balanced designs at distances 1 and 2 (CNBD2), including orthogonal array of type I ($\mathrm{OA}_{I}$) of strength $2$, are the two major designs proposed in literature for the purpose of estimating the direct treatment effects. They are shown to be optimal within some reasonable subclasses of designs. By using benchmark designs in approximate design theory, we show that CNBD2 is highly efficient among all possible designs when the error terms are homoscedastic and uncorrelated. However, when the error terms are correlated, these designs will be outperformed significantly by other designs. Note that CNBD2 fall into the special catalog of pseudo symmetric designs, and they only exist when the number of treatments is larger than the block size and the number of blocks is multiple of some constants. In this paper, we elaborate equivalent conditions for any design, pseudo symmetric or not, to be universally optimal for any size of experiment and any covariance structure of the error terms. This result is novel for circular designs and sheds light on other similar models in the search for optimal or efficient asymmetric designs.