This paper investigates the predictive performance of model averaging in high-dimensional linear regression where the number of regressors is comparable to the sample size. We demonstrate that the double descent trajectory manifests within the model averaging framework, where the ensemble inherits the variance explosion of individual models near the interpolation boundary. However, we reveal that weighted aggregation simultaneously triggers an emergent smoothing effect that structurally suppresses the localized risk divergence, indicating that strategic weight choice serves as a vital stabilizing mechanism. Leveraging tools from random matrix theory, we derive the exact limiting out-of-sample risk under a nested model setting and provide a comprehensive characterization of the risk landscape. Building on these asymptotic results, we propose the Large Model Averaging (LaMA) method, which introduces a novel criterion incorporating in-sample bias and asymptotic out-of-sample variance to balance fitting accuracy and generalization. Numerical studies and real data applications confirm that LaMA achieves superior predictive accuracy in high-dimensional environments.

翻译：本文研究回归变量数量与样本量相当的高维线性回归中模型平均的预测性能。我们证明双重下降轨迹在模型平均框架中显现，当集成模型继承个体模型在插值边界附近的方差爆炸特性时。然而，我们揭示加权聚合同时会触发一种涌现平滑效应，该效应从结构上抑制了局部风险发散，表明策略性权重选择可作为关键稳定机制。利用随机矩阵理论工具，我们在嵌套模型设定下推导出精确的渐近外样本风险，并提供风险景观的全面表征。基于这些渐近结果，我们提出大模型平均方法（LaMA），该方法引入融合样本内偏差与渐近外样本方差的新型准则，以平衡拟合精度与泛化能力。数值实验与真实数据应用证实LaMA在高维环境中能实现更优的预测精度。