# Optimal designs for model averaging in non-nested models

## TL;DR

This paper develops optimal experimental designs for model averaging in non-nested, misspecified models, showing that Bayesian optimal designs significantly enhance estimation accuracy.

## Contribution

It introduces Bayesian optimal designs for model averaging in non-nested models with fixed weights, improving estimation accuracy over traditional methods.

## Key findings

- Bayesian optimal designs reduce mean squared error of estimates.
- Designs improve accuracy for both model averaging and model selection.
- Optimal designs outperform non-optimized designs in simulations.

## 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 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.