TY - JOUR
T1 - Second order statistics of robust estimators of scatter. Application to GLRT detection for elliptical signals
AU - Couillet, Romain
AU - Kammoun, Abla
AU - Pascal, Frédéric
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2015/9/14
Y1 - 2015/9/14
N2 - 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 .
AB - 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 .
UR - http://hdl.handle.net/10754/578817
UR - http://linkinghub.elsevier.com/retrieve/pii/S0047259X15002134
UR - http://www.scopus.com/inward/record.url?scp=84944789716&partnerID=8YFLogxK
U2 - 10.1016/j.jmva.2015.08.021
DO - 10.1016/j.jmva.2015.08.021
M3 - Article
SN - 0047-259X
VL - 143
SP - 249
EP - 274
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
ER -