Asymptotic analysis of a consistent subspace estimator for observations of increasing dimension

Traditional estimators of the eigen-subspaces of sample co-variance matrices are known to be consistent only when the sample volume increases for a fixed observation dimension. Due to this fact, their accuracy tends to be rather poor in practical settings where the number of samples and the observation dimension are comparable in magnitude. To overcome this effect, an estimator was recently proposed that provides consistent subspace estimates even when the dimension of the observation scales up with the number of samples. In this paper, the asymptotic distribution of this estimator is characterized by means of a central limit theorem (CLT).