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Optimality of singular vector perturbation under maximum norm
Author(s) -
Liu Youming,
Qi Xinyu
Publication year - 2020
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.6249
Subject(s) - mathematics , estimator , matrix norm , norm (philosophy) , singular value , estimation of covariance matrices , covariance matrix , singular perturbation , perturbation (astronomy) , matrix (chemical analysis) , covariance , mathematical optimization , mathematical analysis , eigenvalues and eigenvectors , algorithm , statistics , law , physics , materials science , quantum mechanics , political science , composite material
Fan, Wang, and Zhong estimate the difference between the singular vectors of a matrix and those of a perturbed matrix in terms of the maximum norm. Their estimations are used effectively to establish the asymptotic properties of robust covariance estimators (see Journal of Machine Learning Research , 2018;18:1‐42). In this paper, we give the corresponding lower bound estimates, which show Fan‐Wang‐Zhong's estimations optimal.