Optimal minimax designs over a prespecified interval in a heteroscedastic polynomial model.

Minimax optimal designs can be useful for estimating response surface but they are notoriously difficult to study analytically. We provide formulae for three types of minimax optimal designs over a user-specified region. We focus on polynomial models with various types of heteroscedastic errors but the design strategy is applicable to other types of linear models and optimality criteria. Relationships among the three types of minimax optimal designs are discussed.