Estimating the eigenvalues and associated subspaces of correlation matrices from a small number of observations

In this paper, a new method for estimating the eigenvalues and associated subspaces of covariance matrices using their sample estimates is presented. The method is based on random matrix theory and provides consistent estimates when both the sample size and the observation dimension tend to infinity at the same rate, provided that an eigenvalue asymptotic splitting condition is fulfilled. The proposed estimators are shown to have an excellent performance in low sample size scenarios, where the observation dimension and the sample size have the same order of magnitude.