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

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• 作者：Romain Couillet^a ; ^{romain.couillet@supelec.fr" class="auth_mail" title="E-mail the corresponding author} ; Abla Kammoun^b ; ^{abla.kammoun@kaust.edu.sa" class="auth_mail" title="E-mail the corresponding author} ; Fré ; dé ; ric Pascal^a ; ^{frederic.pascal@supelec.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：62H12 ; 60F05 ; 62G35
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：143
• 期：Complete
• 页码：249-274
• 全文大小：755 K

文摘

A central limit theorem for bilinear forms of the type 90bcb727438cb">$a^{\ast }{\hat{C}}_N{\left(\rho \right)}^{-1}b$, where 0b362bcc52f5fd" title="Click to view the MathML source">a,b∈C^N$a,b\in {\mathbb{C}}^N$ are unit norm deterministic vectors and ${\hat{C}}_N\left(\rho \right)$ a robust-shrinkage estimator of scatter parametrized by ρ$\rho$ and built upon n$n$ independent elliptical vector observations, is presented. The fluctuations of 90bcb727438cb">$a^{\ast }{\hat{C}}_N{\left(\rho \right)}^{-1}b$ are found to be of order $N^{-\frac{1}{2}}$ and to be the same as those of $a^{\ast }{\hat{S}}_N{\left(\rho \right)}^{-1}b$ for ${\hat{S}}_N\left(\rho \right)$ 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$\rho$.