The random matrix regime of Maronna's M-estimator for observations corrupted by elliptical noises

Abstract

This article studies the behavior of the Maronna robust scatter estimator ${\hat{C}}_N\in {\mathbb{C}}^{N\times N}$ of a sequence of observations $y_1,...,y_n$ which is composed of a $K$ dimensional signal drown in a heavy tailed noise, i.e $y_i=A_N{s}_i+x_i$ where $A_N\in {\mathbb{C}}^{N\times K}$ and $x_i$ is drawn from elliptical distribution. In particular, we prove that as the population dimension $N$, the number of observations $n$ and the rank of $A_N$ grow to infinity at the same pace and under some mild assumptions, the robust scatter matrix can be characterized by a random matrix ${\hat{S}}_N$ that follows a standard random model. Our analysis can be very useful for many applications of the fields of statistical inference and signal processing.

References in corpus (3)

• Cooperative Spectrum Sensing Using Random Matrix Theory
• Large Dimensional Analysis and Optimization of Robust Shrinkage Covariance Matrix Estimators
• The Random Matrix Regime of Maronna's M-estimator with elliptically distributed samples