Optimal designs for models with block-block resp. treatment-treatment correlations

In this paper the authors study optimal designs assuming two special covariance structures of the observations, namely that the covariance between the observations depends only on the blocks resp. the treatments. They show that the weighted least squares estimator equals the ordinary least squares estimator. Then they prove that block-block correlations resp. treatment-treatment correlations do not have any influence on the A- and MV-optimality resp. A-optimality. For the study of the MV-optimality in the case of treatment-treatment correlations they use the idea of invariance to find optimal C-matrices.