Abstract
We study the behavior of Maronna's robust scatter estimator (C) over cap (N) is an element of C-NxN built from a sequence of observations y(1), . . . , y(n) lying in a K-dimensional signal subspace of the N-dimensional complex field corrupted by heavy tailed noise, i.e., y(i) = A(N)S(l) + x(i), where A(N) is an element of C-NxK and x(i) 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 (S) over cap (N) that follows a standard random model as the population dimension N, the number of observations n, and the rank of A(N) grow to infinity at the same rate. Our results are of potential interest for statistical theory and signal processing. (C) 2017 Elsevier Inc. All rights reserved.