The statistical performance of subspace-based algorithms depends on the deterministic and stochastic statistical model of the noisy linear mixture of the data, the estimate of the projector, and the algorithm that estimates the parameters from the projector. This paper presents different circular and non-circular complex elliptically symmetric (CES) models of the data and different associated non-robust and robust covariance estimators whose asymptotic distributions are derived. This allows us to unify and complement the asymptotic distribution of subspace projectors adapted to these models and to prove several invariance properties that have impacts on the parameters to be estimated in CES data models.