Second order statistics of bilinear forms of robust scatter estimators

Abla Kammoun (1) , Romain Couillet (2) , Frédéric Pascal (2)

1 KAUST - King Abdullah University of Science and Technology [Saudi Arabia]
2 L2S - Laboratoire des signaux et systèmes

This paper lies in the lineage of recent works studying the asymptotic behaviour of robust-scatter estimators in the case where the number of observations and the dimension of the population covariance matrix grow at infinity with the same pace. In particular, we analyze the fluctuations of bilinear forms of the robust schrinkage estimator of covariance matrix. We show that this result can be leveraged in order to improve the design of robust detection methods. As an example, we provide an improved generalized likelihood ratio based detector which combines robustness to impulsive observations and optimality across the shrinkage parameter.

Domaines: Mathématiques [math]; Sciences de l'ingénieur [physics]; Statistiques [stat]

Abla Kammoun, Romain Couillet, Frédéric Pascal. Second order statistics of bilinear forms of robust scatter estimators. 40th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2015), Apr 2015, Brisbane, Australia. ⟨10.1109/ICASSP.2015.7178604⟩. ⟨hal-01262625⟩