Optimal designs for frequentist model averaging

TL;DR

This paper introduces a new optimal design criterion for experiments that improves the accuracy of model averaging estimates in regression analysis under model uncertainty, achieving up to 45% reduction in mean squared error.

Contribution

It proposes a novel optimality criterion for experimental design that minimizes the asymptotic mean squared error of model averaging estimators, with established necessary conditions and practical illustrations.

Findings

Bayesian optimal designs can reduce mean squared error by up to 45%

The new criterion improves estimation accuracy under model uncertainty

Necessary conditions for optimal designs are derived

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 $45\%$.