On the Optimality of Finite Williams II(a) Designs

Abstract

In this paper, we consider the type II(a) designs of Williams. It was shown, essentially, by Kiefer that the type II(a) designs are asymptotically universally optimum for a first order autoregression with parameter $\lambda > 0$. We concentrate on the stationary first order autoregression with $\lambda > 0$ and the extra plot version of the II(a) designs. Our main results are that the design is $D$- and $A$-optimal then, but is not necessarily $E$-optimal when $\lambda$ is small.