Some small and efficient cross - Over designs under a nonadditive model

Abstract

Under a general non-circular, non-additive model which allows for the possible presence of interactions among treatments applied in successive periods, small cross-over designs are proposed. The proposed designs are shown to be optimal for the estimation of carry-over effects while being highly efficient for the direct effects under the stated model. The results are shown to be robust under a random-subject-effect model. Cheng and Wu showed that these designs are optimal for both direct and carry-over effects under an additive model. Our results show that their result for carry-over effects remains robust under non-additive models and also under random-subject effects.