Summary: The design of experiments aims at optimizing certain characteristics of the statistical procedures to be used, in dependence on the settings for the experimental conditions chosen. In particular, certain functionals of the (asymptotic) covariance matrix of the least squares estimator are to be minimized. For multivariate observations designing experiments is substantially more complicated than in univariate settings. If there are additionally many factors of influence which may interact in different ways, the situation becomes even worse. However, by reduction principles, we are able to generate optimal designs for broad classes of multivariate observations in multi-factor settings which will be illustrated here in the case of two factors of influence.
For the entire collection see [Zbl 0866.00051].