The random matrix regime of Maronna's estimator for observations corrupted by elliptical noise

We study the behavior of Maronna's robust scatter estimator CˆN∈CN×N built from a sequence of observations y1,…,yn lying in a K-dimensional signal subspace of theN-dimensional complex field corrupted by heavy tailed noise, i.e., yi=ANsi+xi, where AN∈CN×K and xi is drawn from an elliptical distribution. In particular, we prove under mild assumptions that the robust scatter matrix can be characterized by a random matrix SˆN that follows a standard random model as the population dimension N, the number of observations n, and the rank of AN grow to infinity at the same rate. Our results are of potential interest for statistical theory and signal processing.