TY - GEN
T1 - Tyler's estimator performance analysis
AU - Soloveychik, Ilya
AU - Wiesel, Ami
N1 - Publisher Copyright: © 2015 IEEE.
PY - 2015/8/4
Y1 - 2015/8/4
N2 - This paper analyzes the performance of Tyler's M-estimator of the scatter matrix in elliptical populations. We focus on non-asymptotic performance analysis of Tyler's estimator. Given n samples of dimension p < n, we show that the squared Frobenius norm of the error of the inverse estimator is proportional to p2/(1-c2)2n with high probability, where c is the coherence coefficient of the properly scaled estimator. Under additional group symmetry conditions we improve the obtained bound, utilizing the inherent sparsity properties of group symmetry.
AB - This paper analyzes the performance of Tyler's M-estimator of the scatter matrix in elliptical populations. We focus on non-asymptotic performance analysis of Tyler's estimator. Given n samples of dimension p < n, we show that the squared Frobenius norm of the error of the inverse estimator is proportional to p2/(1-c2)2n with high probability, where c is the coherence coefficient of the properly scaled estimator. Under additional group symmetry conditions we improve the obtained bound, utilizing the inherent sparsity properties of group symmetry.
KW - Elliptical distribution shape matrix estimation
KW - Tyler's scatter estimator
KW - concentration bounds
KW - scatter matrix M-estimators
UR - https://www.scopus.com/pages/publications/84946030099
U2 - 10.1109/ICASSP.2015.7179061
DO - 10.1109/ICASSP.2015.7179061
M3 - Conference contribution
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 5688
EP - 5692
BT - 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
Y2 - 19 April 2014 through 24 April 2014
ER -