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.