Optimality of Certain Asymmetrical Experimental Designs

Abstract

The problem of finding an optimal design for the elimination of one-way heterogeneity when a balanced block design does not exist is studied. A general result on the optimality of certain asymmetrical designs is proved and applied to the block design setting. It follows that if there is a group divisible partially balanced block design (GD PBBD) with 2 groups and $\lambda_2 = \lambda_1 + 1$, then it is optimal w.r.t. a very general class of criteria including all the commonly used ones. On the other hand, if there is a GD PBBD with 2 groups and $\lambda_1 = \lambda_2 + 1$, then it is optimal w.r.t. another class of criteria. Uniqueness of optimal designs and some other miscellaneous results are also obtained.