Large-dimensional behavior of regularized Maronna's M-estimators of covariance matrices

Nicolas Auguin, David Morales-Jimenez, Matthew McKay, Romain Couillet

Research output: Contribution to journalArticle

2 Citations (Scopus)
193 Downloads (Pure)

Abstract

Robust estimators of large covariance matrices are considered, comprising regularized (linear shrinkage) modifi- cations of Maronna’s classical M-estimators. These estimators provide robustness to outliers, while simultaneously being well- defined when the number of samples does not exceed the num- ber of variables. By applying tools from random matrix theory, we characterize the asymptotic performance of such estimators when the numbers of samples and variables grow large together. In particular, our results show that, when outliers are absent, many estimators of the regularized-Maronna type share the same asymptotic performance, and for these estimators we present a data-driven method for choosing the asymptotically optimal regularization parameter with respect to a quadratic loss. Robustness in the presence of outliers is then studied: in the non-regularized case, a large-dimensional robustness metric is proposed, and explicitly computed for two particular types of estimators, exhibiting interesting differences depending on the underlying contamination model. The impact of outliers in regularized estimators is then studied, with remarkable differences with respect to the non-regularized case, leading to new practical insights on the choice of particular estimators.
Original languageEnglish
Pages (from-to)3529-3542
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume66
Issue number13
Early online date30 Apr 2018
DOIs
Publication statusPublished - Jul 2018

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