A1423
Title: High-dimensional factor and clustering analysis via projected and truncated sample covariance matrix
Authors: Long Yu - Shanghai University of Finance and Economics (China) [presenting]
Abstract: Spike identification in high-dimensional mixture factor models is addressed, where spiked eigenvalues of the covariance matrix may arise from clustered mean vectors and/or latent common factors. The magnitudes of the eigenvalues from these two sources can be comparable, posing a significant challenge to model identification and estimation. A novel projected and truncated sample covariance matrix is introduced which, with suitable thresholding, consistently recovers the factor loading space regardless of the relative strength of the cluster-driven eigenvalues. Importantly, this consistency holds even when the subspaces induced by the factor structure and the clustered means are partially confounded. Given the estimated factor space, a projected spectral clustering procedure is proposed that removes the factor component and reveals the underlying cluster structure. Furthermore, an iterative refinement algorithm is developed that builds upon these steps to further enhance estimation accuracy. All proposed methods are supported by rigorous theoretical guarantees and are validated through extensive simulations and real data analyses.
