Large dimensional analysis of Maronna's M-estimator with outliers

David Morales-Jimenez (1) , Romain Couillet (2) , Matthew R. Mckay (1)

1 UniVersity, Nano Science and Technology Program, Department of Chemistry, The Hong Kong UniVersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong,
2 L2S - Laboratoire des signaux et systèmes

Building on recent results in the random matrix analysis of robust estimators of scatter, we show that a certain class of such estimators obtained from samples containing outliers behaves similar to a well-known random matrix model in the limiting regime where both the population and sample sizes grow to infinity at the same speed. This result allows us to understand the structure of such estimators when a certain fraction of the samples is corrupted by outliers and, in particular, to derive their asymptotic eigenvalue distributions. This analysis is a first step towards an improved usage of robust estimation methods under the presence of outliers when the number of independent observations is not too large compared to the size of the population.

Mots clés: Robust estimation; outliers; random matrix theory

Domaines: Mathématiques [math]; Sciences de l'ingénieur [physics]; Statistiques [stat]

David Morales-Jimenez, Romain Couillet, Matthew R. Mckay. Large dimensional analysis of Maronna's M-estimator with outliers. 40th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2015), Apr 2015, Brisbane, Australia. ⟨10.1109/ICASSP.2015.7178605⟩. ⟨hal-01242521⟩