Asymptotic optimality is a key theoretical property in model averaging. Due to technical difficulties, existing studies rely on restricted weight sets or the assumption that there is no true model with fixed dimensions in the candidate set. The focus of this paper is to overcome these difficulties. Surprisingly, we discover that when the penalty factor in the weight selection criterion diverges with a certain order and the true model dimension is fixed, asymptotic loss optimality does not hold, but asymptotic risk optimality does. This result differs from the corresponding result of Fang et al. (2023, Econometric Theory 39, 412-441) and reveals that using the discrete weight set of Hansen (2007, Econometrica 75, 1175-1189) can yield opposite asymptotic properties compared to using the usual weight set. Simulation studies illustrate the theoretical findings in a variety of settings.

翻译：渐近最优性是模型平均中的一个关键理论性质。由于技术困难，现有研究依赖于受限的权重集合或候选集中不存在固定维度的真实模型这一假设。本文的重点在于克服这些困难。令人惊讶的是，我们发现，当权重选择准则中的惩罚因子以特定阶数发散且真实模型维度固定时，渐近损失最优性不成立，但渐近风险最优性成立。这一结果与Fang等人（2023, Econometric Theory 39, 412-441）的相应结论不同，并揭示了使用Hansen（2007, Econometrica 75, 1175-1189）的离散权重集与使用通常的权重集相比，可能产生相反的渐近性质。模拟研究在各种设定下阐明了这些理论发现。