Robust M-estimator of scatter for large elliptical samples

It is shown that Maronna´s robust M-estimator of scatter for elliptical samples behaves similar to an analytically tractable random matrix model in the limiting regime where both the population N and sample n sizes grow to infinity at the same speed. This result allows us to understand the structure of such estimators and in particular to derive their limiting eigenvalue distributions. This analysis is a first step towards an improved usage of robust estimation methods when the number of independent observations is not too large compared to the size of the population.