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

Romain Couillet, Abla Kammoun, Frédéric Pascal

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

A central limit theorem for bilinear forms of the type aĈN-1b, where a,b∈CN are unit norm deterministic vectors and ĈN a robust-shrinkage estimator of scatter parametrized by and built upon n independent elliptical vector observations, is presented. The fluctuations of aĈN-1b are found to be of order N-12 and to be the same as those of aŜN-1b for ŜN 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 .
Original languageEnglish (US)
Pages (from-to)249-274
Number of pages26
JournalJournal of Multivariate Analysis
Volume143
DOIs
StatePublished - Sep 14 2015

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Numerical Analysis

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