A unified approach to the construction of minimax designs

Abstract

We present a unified approach for constructing large-sample optimal designs when the optimality criterion is of the minimax type. The assumed model is a general linear regression model with a known efficiency function defined on a closed and bounded space. An equivalence theorem is formulated and computer algorithms for generating minimax optimal designs are proposed. It is shown that this methodology is simple and rather general. It can be used to construct, for example, minimax variance optimal designs, minimax with respect to the single parameters designs and E-optimal designs. An application of this procedure to find an optimal design for minimizing the maximum predictive variance over a compact region in a heteroscedastic design problem is included.