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. 2019 Sep;106(3):665-682.
doi: 10.1093/biomet/asz036. Epub 2019 Jul 13.

Optimal designs for frequentist model averaging

K Alhorn  1 , K Schorning  2 , H Dette  2
Affiliations

Optimal designs for frequentist model averaging

K Alhorn et al. Biometrika. 2019 Sep.

Abstract

We consider the problem of designing experiments for estimating a target parameter in regression analysis when there is uncertainty about the parametric form of the regression function. A new optimality criterion is proposed that chooses the experimental design to minimize the asymptotic mean squared error of the frequentist model averaging estimate. 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 by up to 45%.

Keywords: Bayesian optimal design; Local misspecification; Model averaging; Model selection; Model uncertainty; Optimal design.

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Figures

Fig. 1.
Fig. 1.
The function formula image in (25) evaluated for (a) the design formula image in (28) and (b) the design formula image in (32).
See this image and copyright information in PMC

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