V-optimal designs for heteroscedastic regression

We obtain V-optimal designs, which minimize the average variance of predicted regression responses, over a finite set of possible regressors. We assume a general and possibly heterogeneous variance structure depending on the design points. The variances are either known (or at least reliably estimated) or unknown. For the former case we exhibit optimal static designs; our methods are then modified to handle the latter case, for which we give a sequential estimation method which is fully adaptive, yielding both consistent variance estimates and an asymptotically V-optimal design.