Local optimality and global superiority of adaptive designs in linear models

An experimental design is called adaptive if the explanatory variables are chosen successively and at a fixed time the choice may be influenced by the results of the experiments up to that time. Adaptive designs are advantageous in non linear problems, when a good or optimal design depends on the true value of the unknown parameters, to achieve an asymptotically optimal design, but also in linear settings. For the latter case we propose a one-step adaptive design which is locally optimal with respect to all Φ_p-criteria, p ≥ 1, and globally superior to nonadaptive designs with respect to the A-criterion.