In this paper, we focus on exploiting the group structure for large-dimensional factor models, which captures the homogeneous effects of common factors on individuals within the same group. In view of the fact that datasets in macroeconomics and finance are typically heavy-tailed, we propose to identify the unknown group structure using the agglomerative hierarchical clustering algorithm and an information criterion with the robust two-step (RTS) estimates as initial values. The loadings and factors are then re-estimated conditional on the identified groups. Theoretically, we demonstrate the consistency of the estimators for both group membership and the number of groups determined by the information criterion. Under finite second moment condition, we provide the convergence rate for the newly estimated factor loadings with group information, which are shown to achieve efficiency gains compared to those obtained without group structure information. Numerical simulations and real data analysis demonstrate the nice finite sample performance of our proposed approach in the presence of both group structure and heavy-tailedness.

翻译：本文聚焦于利用大规模因子模型中的组结构特征，该结构可刻画共同因子对同组个体的同质性影响。鉴于宏观经济和金融数据集通常具有重尾特性，我们提出采用凝聚层次聚类算法与基于稳健两步估计量（RTS）初值的信息准则来识别未知组结构。随后在已识别组结构的条件下重新估计因子载荷与共同因子。理论上，我们证明了基于信息准则的组成员归属和组数估计量的一致性。在有限二阶矩条件下，我们给出了融合组信息的新估计因子载荷的收敛速度，并表明与未利用组结构信息的估计量相比，该估计量可实现效率提升。数值模拟和实际数据分析验证了所提方法在存在组结构与重尾双重挑战时的优异有限样本表现。