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

Abla Kammoun; Mohamed-Slim Alouini

doi:10.1016/j.jmva.2017.08.002

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

Abla Kammoun, Mohamed-Slim Alouini

Research output: Contribution to journal › Article › peer-review

Abstract

We study the behavior of Maronna's robust scatter estimator Cˆ_N∈C^N×N built from a sequence of observations y₁,…,y_n lying in a K-dimensional signal subspace of theN-dimensional complex field corrupted by heavy tailed noise, i.e., y_i=A_Ns_i+x_i, where A_N∈C^N×K 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 Sˆ_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.

Original language	English (US)
Pages (from-to)	51-70
Number of pages	20
Journal	JOURNAL OF MULTIVARIATE ANALYSIS
Volume	162
DOIs	https://doi.org/10.1016/j.jmva.2017.08.002
State	Published - Nov 2017
Externally published	Yes

Keywords

Random matrix theory
Robust scatter estimation
Robust statistics
Signal plus noise model

ASJC Scopus subject areas

Numerical Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.jmva.2017.08.002

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title = "The random matrix regime of Maronna's estimator for observations corrupted by elliptical noise",

abstract = "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.",

keywords = "Random matrix theory, Robust scatter estimation, Robust statistics, Signal plus noise model",

author = "Abla Kammoun and Mohamed-Slim Alouini",

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AU - Kammoun, Abla

AU - Alouini, Mohamed-Slim

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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.

KW - Random matrix theory

KW - Robust scatter estimation

KW - Robust statistics

KW - Signal plus noise model

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

Abstract

Keywords

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