TY - JOUR

T1 - The random matrix regime of Maronna's estimator for observations corrupted by elliptical noise

AU - Kammoun, Abla

AU - Alouini, Mohamed-Slim

N1 - KAUST Repository Item: Exported on 2021-07-09

PY - 2017/8/24

Y1 - 2017/8/24

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/670041

UR - https://linkinghub.elsevier.com/retrieve/pii/S0047259X17304712

UR - http://www.scopus.com/inward/record.url?scp=85033381539&partnerID=8YFLogxK

U2 - 10.1016/j.jmva.2017.08.002

DO - 10.1016/j.jmva.2017.08.002

M3 - Article

AN - SCOPUS:85033381539

VL - 162

SP - 51

EP - 70

JO - JOURNAL OF MULTIVARIATE ANALYSIS

JF - JOURNAL OF MULTIVARIATE ANALYSIS

SN - 0047-259X

ER -