Abstract

I will review some results of an on-going joint research project with Holger Detter and Andrey Pepelyshev. In this project, we propose and develop a new approach to the problem of optimal design for regression experiments with correlated observations. This approach extends the well-known techniques of Bickel-Herzberg and covers the cases of long-range dependence in observations and different asymptotical relations between the number of observations and the size of the design space. In many interesting cases the correlations kernels become singular which implies that traditional methods are no longer applicable. In these cases, a potential theory can be used to derive optimality conditions and establish the existence and uniqueness of the optimal designs. In many instances the optimal designs can be explicitly computed.