  This paper deals with subspace estimation in the small sample size regime,
where the number of samples is comparable in magnitude with the observation
dimension. The traditional estimators, mostly based on the sample correlation
matrix, are known to perform well as long as the number of available samples is
much larger than the observation dimension. However, in the small sample size
regime, the performance degrades. Recently, based on random matrix theory
results, a new subspace estimator was introduced, which was shown to be
consistent in the asymptotic regime where the number of samples and the
observation dimension converge to infinity at the same rate. In practice, this
estimator outperforms the traditional ones even for certain scenarios where the
observation dimension is small and of the same order of magnitude as the number
of samples. In this paper, we address a performance analysis of this recent
estimator, by proving a central limit theorem in the above asymptotic regime.
We propose an accurate approximation of the mean square error, which can be
evaluated numerically.
