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

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.