Optimal designs for model averaging in non-nested models

Abstract

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 derive a necessary condition for the optimality of a given with respect to this new criterion. 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.