On the minimax optimality of non-randomized block designs

In a previous article by the authors (Mathew and Bhaumik (1989)), it was shown that randomization validates (in a minimax sense) the model based optimality results for many designs, for a class of optimality criteria, which includes the A- and E- criteria, but not the D-criterion. In the present paper, it is shown that in the presence of certain model inadequacies, a nonrandomized design can be superior to a randomized design in terms of D-optimality. Motivated by this observation, minimax optimality is investigated for nonrandomized block designs for the A-, D-, and E-criteria.