Title: TransPCA for Large-dimensional Factor Analysis with Weak Factors: Power Enhancement via Knowledge Transfer Show Chinese title

Title: 弱因子的大维因子分析的TransPCA：通过知识迁移增强功率

Abstract: Early work established convergence of the principal component estimators of the factors and loadings up to a rotation for large dimensional approximate factor models with weak factors in that the factor loading $\Lambda^{(0)}$ scales sublinearly in the number $N$ of cross-section units, i.e., $\Lambda^{(0)\top}\Lambda^{(0)}/N^{\alpha}$ is positive definite in the limit for some $\alpha\in (0,1)$. However, the established convergence rates for weak factors can be much slower especially for small $\alpha$. This article proposes a Transfer Principal Component Analysis (TransPCA) method for enhancing the convergence rates for weak factors by transferring knowledge from large number of available informative panel datasets, which should not be turned a blind eye on in this big data era. We aggregate useful information by analyzing a weighted average projection matrix of the estimated loading spaces from all informative datasets which is highly flexible and computationally efficient. Theoretically, we derive the convergence rates of the estimators of weak/strong loading spaces and factor scores. The results indicate that as long as the auxiliary datasets are similar enough to the target dataset and the auxiliary sample size is sufficiently large, TransPCA estimators can achieve faster convergence rates in contrast to performing PCA solely on the target dataset. To avoid negative transfer, we also investigate the case that the informative datasets are unknown and provide a criterion for selecting useful datasets. Thorough simulation studies and {empirical analysis on real datasets in areas of macroeconomic and finance} are conducted to illustrate the usefulness of our proposed methods where large number of source panel datasets are naturally available. Show Chinese abstract

Abstract: 早期的研究证明了大维近似因子模型中主成分估计量（因子和载荷）的收敛性，其中弱因子的载荷矩阵 $\Lambda^{(0)}$ 在截面单元数 $N$ 增长时以次线性方式缩放，即当 $\Lambda^{(0)\top}\Lambda^{(0)}/N^{\alpha}$ 在某种情况下趋于正定矩阵 $\alpha\in (0,1)$ 时成立。 然而，对于弱因子而言，已确立的收敛速度可能非常慢，特别是当 $\alpha$ 较小时。 本文提出了一种迁移主成分分析（TransPCA）方法，通过从大量可用的信息面板数据集中转移知识来提高弱因子的收敛速度，这在大数据时代不应被忽视。 我们通过分析所有信息数据集估计载荷空间的加权平均投影矩阵来聚合有用信息，这种方法具有高度灵活性且计算效率高。 理论上，我们推导出弱/强载荷空间和因子得分估计量的收敛速度。 结果表明，只要辅助数据集与目标数据集足够相似，并且辅助样本量足够大，与仅在目标数据集上执行PCA相比，TransPCA估计量可以实现更快的收敛速度。 为了避免负面迁移，我们还研究了信息数据集未知的情况，并提供了一种选择有用数据集的标准。 进行了全面的模拟研究和 {宏观经济和金融领域真实数据集的经验分析} 来说明我们提出的方法的实用性，在这种情况下，大量的源面板数据集自然可用。