  In this paper we construct optimal designs for frequentist model averaging
estimation. We derive the asymptotic distribution of the model averaging
estimate with fixed weights in the case where the competing models are
non-nested and none of these models is correctly specified. A Bayesian optimal
design minimizes an expectation of the asymptotic mean squared error of the
model averaging estimate calculated with respect to a suitable prior
distribution. We demonstrate that Bayesian optimal designs can improve the
accuracy of model averaging substantially. Moreover, the derived designs also
improve the accuracy of estimation in a model selected by model selection and
model averaging estimates with random weights.
