A new approach to optimal designs for models with correlated observations

Abstract

We consider the problem of designing experiments for the estimation of the mean in the location model in the presence of correlated observations. For a fixed correlation structure approximate optimal designs are determined, and it is demonstrated that under the model assumptions made by Bickel and Herzberg (1979) for the determination of asymptotic optimal design, the designs derived in this paper converge weakly the measures obtained by these authors. We also compare the approach of Sacks and Ylvisaker (1966, 1968) and Bickel and Herzberg (1979) and point out some inconsistencies of the latter. Finally, this approach is modified such that it has similar properties as the model considered by Sacks and Ylvisaker, and it is demonstrated that the resulting design problems are related to (logarithmic) potential theory.