In this article, we present a comprehensive study of asymptotic optimality of least squares model averaging methods. The concept of asymptotic optimality is that in a large-sample sense, the method results in the model averaging estimator with the smallest possible prediction loss among all such estimators. In the literature, asymptotic optimality is usually proved under specific weights restriction or using hardly interpretable assumptions. This article provides a new approach to proving asymptotic optimality, in which a general weight set is adopted, and some easily interpretable assumptions are imposed. In particular, we do not impose any assumptions on the maximum selection risk and allow a larger number of regressors than that of existing studies.

中文翻译：

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最小二乘模型平均渐近最优性的新研究

在本文中，我们对最小二乘模型平均方法的渐近最优性进行了全面研究。渐近最优性的概念是，在大样本意义上，该方法导致模型平均估计器在所有此类估计器中具有最小可能的预测损失。在文献中，渐近最优性通常在特定权重限制或使用难以解释的假设下得到证明。本文提供了一种证明渐近最优性的新方法，其中采用了一般权重集，并施加了一些易于解释的假设。特别是，我们不对最大选择风险强加任何假设，并且允许比现有研究更多的回归变量。