I-robust and D-robust designs on a finite design space

We present and discuss the theory of minimax Iand D-robust designs on a finite design space, and detail three methods for their construction that are new in this context: (i) a numerical search for the optimal parameters in a provably minimax robust parametric class of designs, (ii) a first-order iterative algorithm similar to that of Wynn (Ann Math Stat 5:1655–1664, 1970), and (iii) response-adaptive designs. These designs minimize a loss function, based on the mean squared error of the predicted responses or the parameter estimates, when the regression response is possibly misspecified. The loss function being minimized has first been maximized over a neighbourhood of the approximate and possibly inadequate response being fitted by the experimenter. The methods presented are all vastly more economical, in terms of the computing time required, than previously available algorithms.