Optimal Designs for Model Averaging in non-nested Models

Kira Alhorn, Holger Dette () and Kirsten Schorning
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Kira Alhorn: Technische Universität Dortmund
Holger Dette: Ruhr-Universität Bochum
Kirsten Schorning: Technische Universität Dortmund

Sankhya A: The Indian Journal of Statistics, 2021, vol. 83, issue 2, No 10, 745-778

Abstract: 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. 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 design 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.

Keywords: Model selection; Model averaging; Uniform weighting; Model uncertainty; Optimal design; Bayesian optimal design.; Primary 62K05; Secondary 62F12 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13171-020-00238-9

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