The purpose of this paper is to study optimality of circular neighbor-balanced block designs when neighbor effects are present in the model. In the literature many optimality results are established for direct effects and neighbor effects separately, but few for total effects, that is, the sum of direct effect of treatment and relevant neighbor effects. We show that circular neighbor-balanced designs are universally optimal for total effects among designs with no self neighbor. Then we give efficiency factors of these designs, and show some situations where a design with self neighbors is preferable to a neighbor-balanced design.
"Optimality of neighbor-balanced designs for total effects." Ann. Statist. 32 (4) 1650 - 1661, August 2004. https://doi.org/10.1214/009053604000000481