Second order statistics of bilinear forms of robust scatter estimators
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AbstractThis 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 shrinkage 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, the optimality being considered for the false alarm regulation.
CitationKammoun A, Couillet R, Pascal F (2015) Second order statistics of bilinear forms of robust scatter estimators. 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Available: http://dx.doi.org/10.1109/ICASSP.2015.7178604.
Conference/Event name40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015