MINIMAX DESIGNS IN LINEAR-REGRESSION MODELS

In the usual linear regression model we investigate the geometric structure of a class of minimax optimality criteria containing Elfving's minimax and Kiefer's phi(p)-criteria as special cases. It is shown that the optimal designs with respect to these criteria are also optimal for A'theta, where A is any inball vector (in an appropriate norm) of a generalized Elfving set. The results explain the particular role of the A- and E-optimality criterion and are applied for determining the optimal design with respect to Elfving's minimax criterion in polynomial regression up to degree 9.