Homogeneity and Structure Identification in Semiparametric Factor Models

Factor modeling is an essential tool for exploring intrinsic dependence structures in financial and economic studies through the construction of common latent variables, including the famous Fama–French three factor models for the description of asset returns in finance. However, most of the existing statistical methods for analyzing latent factors have been developed through a linear approach. In this article, we consider a semiparametric factor model and present a regularized estimation procedure for linear component identification on the transformed factor that combines B-spline basis function approximations and the smoothly clipped absolute deviation penalty. In addition, a binary segmentation based algorithm is also developed to identify the homogeneous groups in loading parameters, producing more efficient estimation by pooling information across units within the same group. We carefully derive the asymptotic properties for the proposed procedures. Finally, simulation studies and a real data analysis are conducted to evaluate the finite sample performance of our proposals.因子模型（Factor modeling）是通过构建公共潜变量（latent variable），探究金融与经济研究中内在依赖结构的核心工具，其中涵盖了用于描述金融领域资产收益的经典法玛-弗伦奇三因子模型（Fama–French three factor models）。然而，当前绝大多数用于分析潜因子（latent factor）的统计方法均基于线性范式构建。本文采用半参数因子模型（semiparametric factor model），提出一种针对变换后因子的线性成分识别正则化估计流程，该方法融合了B样条基函数（B-spline basis function）逼近与平滑截断绝对偏差（smoothly clipped absolute deviation）惩罚项。此外，本文还开发了一种基于二元分割（binary segmentation）的算法，用于识别载荷参数（loading parameter）中的同质子组，通过整合同一组别内各单元的信息以实现更高效的估计。我们严格推导了所提方法的渐近性质（asymptotic property）。最后，通过模拟实验与实际数据分析，对本文所提方法的有限样本表现（finite sample performance）进行了评估。