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Article Dans Une Revue Journal of Multivariate Analysis Année : 2016

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

Résumé

A central limit theorem for bilinear forms of the type a * ˆ C N (ρ) −1 b, where a, b ∈ C N are unit norm deterministic vectors and C N (ρ) a robust-shrinkage estima-tor of scatter parametrized by ρ and built upon n independent elliptical vector observations, is presented. The fluctuations of a * ˆ C N (ρ) −1 b are found to be of order N − 1 2 and to be the same as those of a * ˆ S N (ρ) −1 b for S N (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.
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Dates et versions

hal-01262635 , version 1 (26-01-2016)

Identifiants

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Romain Couillet, Abla Kammoun, Frédéric Pascal. Second order statistics of robust estimators of scatter. Application to GLRT detection for elliptical signals. Journal of Multivariate Analysis, 2016, 143, pp.249-274. ⟨10.1016/j.jmva.2015.08.021⟩. ⟨hal-01262635⟩
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