Once more: optimal experimental design for regression models (with discussion)

Abstract

The paper reconsiders some of the recent developments in experimental design for linear regression models. Atfirst, some attention is paid to a discussion of the advantages and limitations of a decision–theoretically oriented approach to the compound problem including the choice of set–up, estimator and experimental design, with special emphasis on the use of prior knowledge and on robustness inverstigations. In the main part of the paraper we review and discuss our results obtained since 1979 concerning BAYESian experimental design and experimental design in case of correalted observations. As a main feaurer we can point out an analogy between continuous experimental designing and linear regression estimation which opens the possibility to use experimental designs methods for the ocnstructions of optimal lineal estimators. This is demosntrated, in praticular, for the fields of minimaz linear estiamtion with a restircted parameter space and best linear unbiased estimation of the trend functions of random processes