In this paper, we study transfer learning for high-dimensional factor-augmented sparse linear models, motivated by applications in economics and finance where strongly correlated predictors and latent factor structures pose major challenges for reliable estimation. Our framework simultaneously mitigates the impact of high correlation and removes the additional contributions of latent factors, thereby reducing potential model misspecification in conventional linear modeling. In such settings, the target dataset is often limited, but multiple heterogeneous auxiliary sources may provide additional information. We develop transfer learning procedures that effectively leverage these auxiliary datasets to improve estimation accuracy, and establish non-asymptotic $\ell_1$- and $\ell_2$-error bounds for the proposed estimators. To prevent negative transfer, we introduce a data-driven source detection algorithm capable of identifying informative auxiliary datasets and prove its consistency. In addition, we provide a hypothesis testing framework for assessing the adequacy of the factor model, together with a procedure for constructing simultaneous confidence intervals for the regression coefficients of interest. Numerical studies demonstrate that our methods achieve substantial gains in estimation accuracy and remain robust under heterogeneity across datasets. Overall, our framework offers a theoretical foundation and a practically scalable solution for incorporating heterogeneous auxiliary information in settings with highly correlated features and latent factor structures.

翻译：本文研究高维因子增强稀疏线性模型的迁移学习，其动机源于经济学和金融学中的应用——在这些领域中，强相关预测变量和潜在因子结构对可靠估计构成了主要挑战。我们的框架能同时缓解高相关性的影响，并消除潜在因子的额外贡献，从而减少传统线性建模中潜在的模型误设风险。在此类设定下，目标数据集通常有限，但多个异质性辅助源可能提供额外信息。我们开发了能有效利用这些辅助数据集以提高估计精度的迁移学习程序，并为所提出的估计量建立了非渐近的$\ell_1$和$\ell_2$误差界。为防止负迁移，我们引入了一种能够识别信息性辅助数据集的数据驱动源检测算法，并证明了其一致性。此外，我们还提供了用于评估因子模型充分性的假设检验框架，以及为感兴趣回归系数构建联合置信区间的程序。数值研究表明，我们的方法在估计精度上实现了显著提升，并在数据集异质性下保持稳健。总体而言，我们的框架为在具有高度相关特征和潜在因子结构的设定中融合异质性辅助信息提供了理论基础和实际可扩展的解决方案。