Some Properties of Exchange Design Algorithms Under Correlation

In this paper we discuss an algorithm for the construction of D-optimal experimental designs for the parameters in a regression model when the errors have a correlation structure. We show that design points can collapse under the presence of some covariance structures and a so called nugget can be employed in a natural way. We also show that the information of equidistant design on covariance parameter is increasing with the number of design points under exponential variogram, however these designs are not D-optimal. Also in higher dimensions the exponential structure without nugget leads to collapsing of the D-optimal design when also parameters of covariance structure are of interest. However, if only trend parameters are of interest, the designs covering uniformly the whole design space are very efficient. For illustration some numerical examples are also included. (author's abstract)