Optimal non‐circular designs for interference models

Abstract

In many applications of block designs, the responses of plots are affected by treatments in neighbouring plots. What makes it more complicated is the border effect on the two edge plots caused by potential environmental impacts outside the blocks. For the latter, many researchers use two guarding plots next to the edge plots, for which we apply certain treatments to control these impacts. There have been extensive studies of designs under this set‐up; however, we observe that existing literature has been focusing on circular designs where the treatments applied to the border effects are the same as the edge plots on their opposite sides. This structural restriction is unnecessary in most applications. We consider non‐circular designs, where guarding plots are allowed to take any treatments by design. In this paper, optimal non‐circular designs are constructed for direct effects estimations. It is found that optimal non‐circular designs outperform optimal circular designs in many cases, especially for many commonly studied cases in the literature.