Second order statistics of robust estimators of scatter. Application to GLRT detection for elliptical signals

Romain Couillet, Abla Kammoun and Frédéric Pascal

Journal of Multivariate Analysis, 2016, vol. 143, issue C, 249-274

Abstract: A central limit theorem for bilinear forms of the type a∗CˆN(ρ)−1b, where a,b∈CN are unit norm deterministic vectors and CˆN(ρ) a robust-shrinkage estimator of scatter parametrized by ρ and built upon n independent elliptical vector observations, is presented. The fluctuations of a∗CˆN(ρ)−1b are found to be of order N−12 and to be the same as those of a∗SˆN(ρ)−1b for SˆN(ρ) a matrix of a theoretical tractable form. This result is exploited in a classical signal detection problem to provide an improved detector which is both robust to elliptical data observations (e.g., impulsive noise) and optimized across the shrinkage parameter ρ.

Keywords: Random matrix theory; Robust estimation; Central limit theorem; GLRT (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.jmva.2015.08.021

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