DocumentCode
67077
Title
Performance Analysis of Tyler´s Covariance Estimator
Author
Soloveychik, Ilya ; Wiesel, Ami
Author_Institution
Rachel & Selim Benin Sch. of Comput. Sci. & Eng., Hebrew Univ. of Jeursalem, Jeursalem, Israel
Volume
63
Issue
2
fYear
2015
fDate
Jan.15, 2015
Firstpage
418
Lastpage
426
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.
Keywords
S-matrix theory; covariance analysis; covariance matrices; estimation theory; probability; signal sampling; Tyler M-estimator; Tyler covariance estimator performance analysis; elliptical population; inverse estimator decay; nonasymptotic setting; probability; scatter matrix; squared Frobenius norm; Covariance matrices; Maximum likelihood estimation; Performance analysis; Robustness; Shape; Vectors; Concentration bounds; Tyler´s scatter estimator; elliptical distribution shape matrix estimation; scatter matrix M-estimators;
fLanguage
English
Journal_Title
Signal Processing, IEEE Transactions on
Publisher
ieee
ISSN
1053-587X
Type
jour
DOI
10.1109/TSP.2014.2376911
Filename
6971237
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