Tyler's estimator performance analysis
Abstract
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 p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /(1-c <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> n 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.
BibTeX
@inproceedings{icassp2015_tylersestimatorp,
title = {Tyler's estimator performance analysis},
author = {Ilya Soloveychik and Ami Wiesel},
booktitle = {ICASSP 2015},
year = {2015}
}