Optimal nested row-column designs with specified components

Abstract

We consider nested row-column designs where each of the row and column component designs is specified. For the case that each of the component designs has second-order balance, we define such a nested row-column design to be special if it is generally balanced, with the smallest possible number of canonical treatment contrasts having the lower canonical efficiency factor in both components. We show that if any special row-column design exists then it is A-optimal over all nested row-column designs with the given components.