Optimality of k-proportional designs for simultaneous inference

Abstract

In the ANOVA setup with K factors without interactions the optimum design problem for simultaneous inference on the basic contrasts of the first k<K factors is considered. It is shown that k-proportional designs are uniformly optimal in some (small) class of designs and, with an additional condition, are D-optimal in the class of N-observation designs and that there are no other optimal designs provid3ed these designs exist. It also turns out that these designs have an additional constrained optimality property.

Keywords:

• k-proportional designs
• ANOVA setup
• U-optimality
• D-optimality
• repeated measurements designs
• constrained optimality