Tyler´s estimator performance analysis

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.