Some results on optimal design under a first-order autoregression and on finite williams type ii designs

It was shown, essentially, by Kiefer (1961) that the type II (a) design of Williams (1952) is asymptotically universally optimum for a first-order autoregression with parameter λ >0. We investigate any optimality properties these designs have when finite. We show that small differences in the definitions of the autoregression or of the design can lead to standard results in the theory of optiaml design no longer being applicable. We include some useful results on patterned matrices.