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%.

中文翻译：

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频率模型平均的优化设计

当回归函数的参数形式存在不确定性时，我们考虑设计用于估计回归分析中的目标参数的实验问题。提出了一种新的最优性准则，该准则选择实验设计以最小化频率模型平均估计的渐近均方误差。建立了局部和贝叶斯优化设计问题的最优解的必要条件。结果在几个示例中进行了说明，并且证明贝叶斯优化设计可以将模型平均估计器的均方误差降低多达 45%。