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Rigorous stochastic bounds for the error in large covariance matrices
Author(s) -
Böttcher Albrecht,
Wenzel David
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.969
Subject(s) - mathematics , covariance , eigenvalues and eigenvectors , dimension (graph theory) , covariance matrix , random matrix , norm (philosophy) , matrix norm , matrix (chemical analysis) , covariance function , infinity , pure mathematics , combinatorics , statistics , mathematical analysis , physics , materials science , quantum mechanics , political science , law , composite material
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 © 2007 John Wiley & Sons, Ltd.
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