Universal Optimality Designs

Abstract

In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design on the other hand requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design. Thus in practical terms, optimal experiments can reduce the costs of experimentation. We construct an optimal design among a family of designs,, with b=5 blocks of size k=5 and with t=5 treatments. We demonstrate that such a design is optimal under all the optimality criteria considered by Kiefer (1975). It is thus universally optimal.