Robust shrinkage M-estimators of large covariance matrices

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

Abstract:
Robust high dimensional covariance estimators are considered, comprising regularized (linear shrinkage) modifications of Maronna's classical M-estimators. Such estimators aim to provide robustness to outliers, while simultaneously giving well-defined solutions under high dimensional scenarios where the number of samples does not exceed the number of variables. By applying tools from random matrix theory, we characterize the asymptotic performance of such estimators when the number of samples and variables grow large together. In particular, our results show that, when outliers are absent, many estimators of the shrinkage-Maronna type share the same asymptotic performance, and for such estimators we present a data-driven method for choosing the asymptotically optimal shrinkage parameter. Although our results assume an outlier-free scenario, simulations suggest that certain estimators perform substantially better than others when subjected to outlier samples.
Original languageEnglish
Title of host publicationIEEE Statistical Signal Processing Workshop (SSP) 2016: Proceedings
Publisher IEEE
Number of pages4
ISBN (Electronic)978-1-4673-7803-1
ISBN (Print)978-1-4673-7804-8
DOIs
Publication statusPublished - 25 Aug 2016

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    Auguin, N., Morales-Jimenez, D., McKay, M., & Couillet, R. (2016). Robust shrinkage M-estimators of large covariance matrices. In IEEE Statistical Signal Processing Workshop (SSP) 2016: Proceedings IEEE . https://doi.org/10.1109/SSP.2016.7551720