z-logo
Premium
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.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here