Tyler's estimator performance analysis

Ilya Soloveychik; Ami Wiesel

doi:10.1109/ICASSP.2015.7179061

Tyler's estimator performance analysis

Ilya Soloveychik, Ami Wiesel

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

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 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.

Original language	English
Title of host publication	2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5688-5692
Number of pages	5
ISBN (Electronic)	9781467369978
DOIs	https://doi.org/10.1109/ICASSP.2015.7179061
State	Published - 4 Aug 2015
Event	40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Brisbane, Australia Duration: 19 Apr 2014 → 24 Apr 2014

Publication series

Name	ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume	2015-August
ISSN (Print)	1520-6149

Conference

Conference	40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015
Country/Territory	Australia
City	Brisbane
Period	19/04/14 → 24/04/14

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

Keywords

Elliptical distribution shape matrix estimation
Tyler's scatter estimator
concentration bounds
scatter matrix M-estimators

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10.1109/ICASSP.2015.7179061

Cite this

Soloveychik, I., & Wiesel, A. (2015). Tyler's estimator performance analysis. In 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings (pp. 5688-5692). Article 7179061 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2015-August). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2015.7179061

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Soloveychik, I & Wiesel, A 2015, Tyler's estimator performance analysis. in 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings., 7179061, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. 2015-August, Institute of Electrical and Electronics Engineers Inc., pp. 5688-5692, 40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015, Brisbane, Australia, 19/04/14. https://doi.org/10.1109/ICASSP.2015.7179061

Tyler's estimator performance analysis. / Soloveychik, Ilya; Wiesel, Ami.
2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2015. p. 5688-5692 7179061 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2015-August).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Soloveychik I, Wiesel A. Tyler's estimator performance analysis. In 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2015. p. 5688-5692. 7179061. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). doi: 10.1109/ICASSP.2015.7179061

Tyler's estimator performance analysis

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Keywords

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