Compromise estimation entails using a weighted average of outputs from several candidate models, and is a viable alternative to model selection when the choice of model is not obvious. As such, it is a tool used by both frequentists and Bayesians, and in both cases, the literature is vast and includes studies of performance in simulations and applied examples. However, frequentist researchers often prove oracle properties, showing that a proposed average asymptotically performs at least as well as any other average comprising the same candidates. On the Bayesian side, such oracle properties are yet to be established. This paper considers Bayesian stacking estimators, and evaluates their performance using frequentist asymptotics. Oracle properties are derived for estimators stacking Bayesian linear and logistic regression models, and combined with Monte Carlo experiments that show Bayesian stacking may outperform the best candidate model included in the stack. Thus, the result is not only a frequentist motivation of a fundamentally Bayesian procedure, but also an extended range of methods available to frequentist practitioners.

翻译：折衷估计涉及使用多个候选模型输出的加权平均，当模型选择不明显时，它是模型选择的一种可行替代方案。因此，它是频率主义者和贝叶斯主义者都使用的工具，在这两种情况下，文献都非常丰富，包括模拟和应用实例中的性能研究。然而，频率主义研究者经常证明Oracle性质，表明所提出的平均估计量在渐近意义上至少与由相同候选模型组成的任何其他平均估计量表现一样好。在贝叶斯方面，此类Oracle性质尚未得到确立。本文考虑贝叶斯堆叠估计量，并使用频率主义渐近理论评估其性能。我们推导了堆叠贝叶斯线性回归和逻辑回归模型的估计量的Oracle性质，并结合蒙特卡洛实验表明贝叶斯堆叠可能优于堆叠中包含的最佳候选模型。因此，该结果不仅为一种本质上是贝叶斯的过程提供了频率主义动机，也为频率主义实践者提供了更广泛的方法选择。