Does Principal Component Analysis Preserve the Sparsity in Sparse Weak Factor Models?
主成分分析能否保留稀疏弱因子模型的稀疏性?
This paper studies the principal component (PC) method-based estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PC estimators of loadings, which comes from the approximately upper triangular (block) structure of the rotation matrix. It implies an asymmetric relationship among factors: the rotated loadings for a stronger factor can be contaminated by those from a weaker one, but the loadings for a weaker…