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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.