The random matrix regime of Maronna’s M-estimator with elliptically distributed samples

Romain Couillet, Frédéric Pascal and Jack W. Silverstein

Journal of Multivariate Analysis, 2015, vol. 139, issue C, 56-78

Abstract: This article demonstrates that the robust scatter matrix estimator CˆN∈CN×N of a multivariate elliptical population x1,…,xn∈CN originally proposed by Maronna in 1976, and defined as the solution (when existent) of an implicit equation, behaves similar to a well-known random matrix model in the limiting regime where the population N and sample n sizes grow at the same speed. We show precisely that CˆN∈CN×N is defined for all n large with probability one and that, under some light hypotheses, ‖CˆN−SˆN‖→0 almost surely in spectral norm, where SˆN follows a classical random matrix model. As a corollary, the limiting eigenvalue distribution of CˆN is derived. This analysis finds applications in the fields of statistical inference and signal processing.

Keywords: Random matrix theory; Robust estimation; Elliptical distribution (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (7)

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DOI: 10.1016/j.jmva.2015.02.020

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