On adaptive EVD asymptotic distribution of centro-symmetric covariance matrices

This article investigates the gain in statistical performance/complexity of the adaptive estimation of the eigenvalue decomposition (EVD) of covariance matrices when the centro-symmetric (CS) structure of such matrices is utilized. After deriving the asymptotic distribution of the EVD estimators, it is shown, in particular, that the closed-form expressions for the asymptotic covariance of batch and adaptive EVD estimators are very similar, provided that the number of samples is replaced by the inverse of the step size.