On the Convergence of Maronna's M-Estimators of Scatter

被引:2
|
作者
Chitour, Yacine [1 ,2 ]
Couillet, Romain [3 ]
Pascal, Frederic [4 ]
机构
[1] Supelec, Signaux & Syst Lab, F-91192 Gif Sur Yvette, France
[2] Univ Paris 11, Orsay, France
[3] Supelec, Dept Telecommun, F-91192 Gif Sur Yvette, France
[4] Supelec, SONDRA Lab, F-91192 Gif Sur Yvette, France
关键词
Covariance matrix estimation; M-estimators; Tyler's estimator; MULTIVARIATE LOCATION; ALGORITHM ANALYSIS; EXISTENCE;
D O I
10.1109/LSP.2014.2367547
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
In this letter, we propose an alternative proof for the uniqueness of Maronna's M-estimator of scatter [1] for vector observations y(1),...,y(N) is an element of R-m under a mild constraint of linear independence of any subset of of these vectors. This entails in particular almost sure uniqueness for random vectors y(i) with a density as long as N > m. This approach allows to establish further relations that demonstrate that a properly normalized Tyler's M-estimator of scatter [2] can be considered as a limit of Maronna's M-estimator. More precisely, the contribution is to show that each M-estimator, verifying some mild conditions, converges towards a particular Tyler's M-estimator. These results find important implications in recent works on the large dimensional (random matrix) regime of robust M-estimation.
引用
收藏
页码:709 / 712
页数:4
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