Large Dimensional Analysis of Robust M-Estimators of Covariance With Outliers - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue IEEE Transactions on Signal Processing Année : 2015

Large Dimensional Analysis of Robust M-Estimators of Covariance With Outliers

Résumé

A large dimensional characterization of robust M-estimators of covariance (or scatter) is provided under the assumption that the dataset comprises independent (essentially Gaussian) legitimate samples as well as arbitrary deterministic samples, referred to as outliers. Building upon recent random matrix advances in the area of robust statistics, we specifically show that the so-called Maronna M-estimator of scatter asymp-totically behaves similar to well-known random matrices when the population and sample sizes grow together to infinity. The introduction of outliers leads the robust estimator to behave asymptotically as the weighted sum of the sample outer products, with a constant weight for all legitimate samples and different weights for the outliers. A fine analysis of this structure reveals importantly that the propensity of the M-estimator to attenuate (or enhance) the impact of outliers is mostly dictated by the alignment of the outliers with the inverse population covariance matrix of the legitimate samples. Thus, robust M-estimators can bring substantial benefits over more simplistic estimators such as the per-sample normalized version of the sample covariance matrix, which is not capable of differentiating the outlying samples. The analysis shows that, within the class of Maronna's estimators of scatter, the Huber estimator is most favorable for rejecting outliers. On the contrary, estimators more similar to Tyler's scale invariant estimator (often preferred in the literature) run the risk of inadvertently enhancing some outliers.
Fichier principal
Vignette du fichier
1503.01245(1).pdf (322.53 Ko) Télécharger le fichier
Origine Accord explicite pour ce dépôt
Loading...

Dates et versions

hal-01242442 , version 1 (12-12-2015)

Identifiants

Citer

David Morales-Jimenez, Romain Couillet, Matthew Mckay. Large Dimensional Analysis of Robust M-Estimators of Covariance With Outliers. IEEE Transactions on Signal Processing, 2015, 63 (21), pp.5784 -5797. ⟨10.1109/TSP.2015.2460225⟩. ⟨hal-01242442⟩
127 Consultations
114 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More