This paper analyzes the performance of Tyler's M-estimator of the scatter matrix in elliptical populations. We focus on the non-asymptotic setting and derive estimation error bounds depending on the number of samples n and the dimension p. We show that under mild conditions the squared Frobenius norm of the error of the inverse estimator decays like p2/n with high probability.
Bibliographical notePublisher Copyright:
© 2014 IEEE.
- Concentration bounds
- Tyler's scatter estimator
- elliptical distribution shape matrix estimation
- scatter matrix M-estimators