CAN PRINCIPAL COMPONENT ANALYSIS PRESERVE THE SPARSITY IN FACTOR LOADINGS?
研究了弱因子模型中主成分分析估计载荷的稀疏保持性质，发现旋转矩阵的近似块上三角结构导致因子间不对称关系，并提出一种简单的筛选方法直接稀疏化载荷估计。
This article studies the principal component analysis (PCA) estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PCA estimators of loadings, which comes from the approximately (block) upper triangular structure of the rotation matrix. It suggests an asymmetric relationship among factors: the sparsity of the rotated loadings for a stronger factor can be contaminated by the loadings from weaker ones, but the sparsity of the rotated loadings of a weaker factor is almost unaffected by the loadings of stronger ones. Then, we propose a simple alternative to the existing penalized approaches to sparsify the loading estimators by screening out the small PCA loading estimators directly, and construct consistent estimators for factor strengths. The proposed estimators perform well in finite samples, as shown by a set of Monte Carlo simulations.