Performance analysis of Tyler's covariance estimator

Ilya Soloveychik; Ami Wiesel

doi:https://doi.org/10.1109/TSP.2014.2376911

Performance analysis of Tyler's covariance estimator

Ilya Soloveychik, Ami Wiesel

The Rachel and Selim Benin School of Engineering and Computer Science

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	6971237
Pages (from-to)	418-426
Number of pages	9
Journal	IEEE Transactions on Signal Processing
Volume	63
Issue number	2
DOIs	https://doi.org/10.1109/TSP.2014.2376911
State	Published - 15 Jan 2015

Keywords

Concentration bounds
Tyler's scatter estimator
elliptical distribution shape matrix estimation
scatter matrix M-estimators

All Science Journal Classification (ASJC) codes

Signal Processing
Electrical and Electronic Engineering

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abstract = "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.",

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KW - elliptical distribution shape matrix estimation

KW - scatter matrix M-estimators

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Performance analysis of Tyler's covariance estimator

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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