  The estimation of large covariance matrices has a high dimensional bias.
Correcting for this bias can be reformulated via the tool of Free Probability
Theory as a free deconvolution.
  The goal of this work is a computational and statistical resolution of this
problem. Our approach is based on complex-analytic methods methods to invert
$S$-transforms. In particular, one needs a theoretical understanding of the
Riemann surfaces where multivalued $S$ transforms live and an efficient
computational scheme.
