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

Access to Document

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

@inproceedings{a2b5b0988e3c40978089e7f5625f183f,

title = "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 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.",

keywords = "Elliptical distribution shape matrix estimation, Tyler's scatter estimator, concentration bounds, scatter matrix M-estimators",

author = "Ilya Soloveychik and Ami Wiesel",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.; 40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 ; Conference date: 19-04-2014 Through 24-04-2014",

year = "2015",

month = aug,

day = "4",

doi = "10.1109/ICASSP.2015.7179061",

language = "אנגלית",

series = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "5688--5692",

booktitle = "2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings",

address = "ארצות הברית",

}

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

TY - GEN

T1 - Tyler's estimator performance analysis

AU - Soloveychik, Ilya

AU - Wiesel, Ami

PY - 2015/8/4

Y1 - 2015/8/4

N2 - 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.

AB - 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.

KW - Elliptical distribution shape matrix estimation

KW - Tyler's scatter estimator

KW - concentration bounds

KW - scatter matrix M-estimators

UR - https://www.scopus.com/pages/publications/84946030099

U2 - 10.1109/ICASSP.2015.7179061

DO - 10.1109/ICASSP.2015.7179061

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:84946030099

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - 5688

EP - 5692

BT - 2015 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015

Y2 - 19 April 2014 through 24 April 2014

ER -

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

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this