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

2014/10/03 by Romain Couillet, Couillet, Romain, Abla Kammoun +3 · 1 citation
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Image and Signal Denoising Methods #Infrared Target Detection Methodologies #Probability (math.PR) #Radar Systems and Signal Processing #Random Matrices and Applications #Sparse and Compressive Sensing Techniques #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.1410.0817

openalex publication_date 2014/10/03 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

A central limit theorem for bilinear forms of the type\na^*\C_N(\ρ)^-1b, where a,b\∈ mathbb C^N are unit norm\ndeterministic vectors and \C_N(\ρ) a robust-shrinkage estimator of\nscatter parametrized by \ρ and built upon n independent elliptical vector\nobservations, is presented. The fluctuations of a^*\C_N(\ρ)^-1b are\nfound to be of order N^{- frac12} and to be the same as those of\na^*\S_N(\ρ)^-1b for \S_N(\ρ) a matrix of a theoretical\ntractable form. This result is exploited in a classical signal detection\nproblem to provide an improved detector which is both robust to elliptical data\nobservations (e.g., impulsive noise) and optimized across the shrinkage\nparameter \ρ.\n

Citations

• A New Approach for Capacity Analysis of Large Dimensional Multi-Antenna Channels
• A Distribution-Free M-Estimator of Multivariate Scatter
• Foundations of Modern Probability
• On the Empirical Distribution of Eigenvalues of a Class of Large Dimensional Random Matrices
• A well-conditioned estimator for large-dimensional covariance matrices
• Asymptotic behavior of unregularized and ridge-regularized high-dimensional robust regression estimators : rigorous results

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