Rigorous stochastic bounds for the error in large covariance matrices

摘要

This paper is motivated by recent studies of Huang et al. on distributed PCA and network anomaly detection and contains a rigorous derivation of bounds for the expected value and the variance of the spectral norm of the error in large covariance matrices. This derivation is based on a deep result by Yin et al. (Probab. Theor. Relat. Fields 1988; 78:509-521), which gives the asymptotics of the maximal eigenvalue of a random matrix as the matrix dimension goes to infinity. Copyright (C) 2007 John Wiley & Sons, Ltd.