  We consider the problem of designing experiments for the estimation of a
target in regression analysis if there is uncertainty about the parametric form
of the regression function. A new optimality criterion is proposed, which
minimizes the asymptotic mean squared error of the frequentist model averaging
estimate by the choice of an experimental design. Necessary conditions for the
optimal solution of a locally and Bayesian optimal design problem are
established. The results are illustrated in several examples and it is
demonstrated that Bayesian optimal designs can yield a reduction of the mean
squared error of the model averaging estimator up to $45\%$.
