Efficiency of subspace-based estimators for elliptical symmetric distributions

•Asymptotic (in the number of measurements) distributions of estimates of the orthogonal projector associated with different M-estimates of the covariance matrix in the context of RES, C-CES, and NC-CES distributed observations whose covariance is low rank structured are given in the same framework.•The asymptotically minimum variance (AMV) subspace-based estimator of the parameter of interest characterized by the column subspace of the mixing matrix for general linear mixtures models, associated with the M-estimates of the covariance matrix is derived.•A common closed-form expression of the AMV bound which can be used as a benchmark against which any subspace-based algorithms are tested is derived.•It is proved that the AMV bound attains the stochastic CRB in the case of ML M-estimate of the covariance matrix for RES, C-CES, and NC-CES distributed observations•We specify the conditions for which the AMV bound based on Tyler’s M-estimate attains this stochastic CRB for complex Student t and complex generalized Gaussian distributions.•It is proved that the stochastic CRB is equal to the semiparametric CRB recently introduced for this model.