MV-optimal block designs for correlated errors

This paper presents MV-optimal block designs for three treatments having b=3n+1 blocks each of size three when observations within each block are correlated. Two distinct covariance structures are considered, and the optimality problem is addressed using generalized least squares estimation of treatment contrasts in fixed-block effects model. In particular, it is shown that a design d∗ having n copies of the blocks (1, 2, 3), (2, 3, 1), (3, 1, 2) and one copy of (1, 3, 2) is MV-optimal within the class of all equally replicated connected designs. A class of unequally replicated designs is found to be MV-better than d∗ in the unrestricted class of all connected designs for large positive correlations.