On Universal Optimality of Circular Weakly Neighbor Balanced Designs Under an Interference Model

Abstract

In this article, the optimal design problem in a fixed effects interference model with left-neighbor effects is studied. It is known (Druilhet, 1999) that circular neighbor balanced designs (CNBDs) are universally optimal in such a model. We prove the universal optimality of circular weakly neighbor balanced designs (CWNBDs), which require a smaller number of blocks than CNBDs. CWNBDs with the number of blocks smaller than the number of treatments belong to the class of partially neighbor balanced designs (PNBDs) defined by Wilkinson et al. (1983). We give a construction method for some CWNBDs, with examples.

Keywords:

• Circular neighbor balanced design
• Circular weakly neighbor balanced design
• Information matrix
• Interference model
• Universal optimality

Mathematics Subject Classification:

• 62K05
• 62K01