Optimal designs for frequentist model averaging
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Date
2018
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Abstract
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%.
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Keywords
model selection, Bayesian optimal designs, optimal design, model uncertainty, local misspecification, model averaging