Model averaging has gained significant attention in recent years due to its ability of fusing information from different models. The critical challenge in frequentist model averaging is the choice of weight vector. The bootstrap method, known for its favorable properties, presents a new solution. In this paper, we propose a bootstrap model averaging approach that selects the weights by minimizing a bootstrap criterion. Our weight selection criterion can also be interpreted as a bootstrap aggregating. We demonstrate that the resultant estimator is asymptotically optimal in the sense that it achieves the lowest possible squared error loss. Furthermore, we establish the convergence rate of bootstrap weights tending to the theoretically optimal weights. Additionally, we derive the limiting distribution for our proposed model averaging estimator. Through simulation studies and empirical applications, we show that our proposed method often has better performance than other commonly used model selection and model averaging methods, and bootstrap variants.

翻译：近年来，模型平均法因其能够融合不同模型的信息而受到广泛关注。频率学派模型平均中的关键挑战在于权重向量的选择。以优良特性著称的Bootstrap方法为此提供了新的解决方案。本文提出一种Bootstrap模型平均方法，通过最小化Bootstrap准则来选择权重。我们的权重选择准则亦可解释为Bootstrap聚合。我们证明所得估计量具有渐近最优性，即能达到可能的最小平方误差损失。此外，我们建立了Bootstrap权重收敛于理论最优权重的收敛速率，并推导了所提模型平均估计量的极限分布。通过模拟研究和实证应用，我们表明所提方法通常优于其他常用的模型选择、模型平均方法以及Bootstrap变体。