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Journal articles
On the Convergence of Maronna's M-Estimators of Scatter
Abstract : In this letter, we propose an alternative proof for the uniqueness of Maronna's M-estimator of scatter [1] for vector observations under a mild constraint of linear independence of any subset of of these vectors. This entails in particular almost sure uniqueness for random vectors with a density as long as. This approach allows to establish further relations that demonstrate that a properly normalized Tyler's-estimator of scatter [2] can be considered as a limit of Maronna's M-estimator. More precisely, the contribution is to show that each-estimator, verifying some mild conditions, converges towards a particular Tyler's-estimator. These results find important implications in recent works on the large dimensional (random matrix) regime of robust-estimation.
Cited literature [17 references]
https://hal-centralesupelec.archives-ouvertes.fr/hal-01251753
Contributor : Frédéric Pascal Connect in order to contact the contributor
Submitted on : Wednesday, February 26, 2020 - 10:56:05 AM
Last modification on : Thursday, October 14, 2021 - 9:15:51 AM
Long-term archiving on: : Wednesday, May 27, 2020 - 2:54:06 PM
Contributor : Frédéric Pascal Connect in order to contact the contributor
Submitted on : Wednesday, February 26, 2020 - 10:56:05 AM
Last modification on : Thursday, October 14, 2021 - 9:15:51 AM
Long-term archiving on: : Wednesday, May 27, 2020 - 2:54:06 PM
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