  We derive an optimal shrinkage sample covariance matrix (SCM) estimator which
is suitable for high dimensional problems and when sampling from an unspecified
elliptically symmetric distribution. Specifically, we derive the optimal
(oracle) shrinkage parameters that obtain the minimum mean-squared error (MMSE)
between the shrinkage SCM and the true covariance matrix when sampling from an
elliptical distribution. Subsequently, we show how the oracle shrinkage
parameters can be consistently estimated under the random matrix theory regime.
Simulations show the advantage of the proposed estimator over the conventional
shrinkage SCM estimator due to Ledoit and Wolf (2004). The proposed shrinkage
SCM estimator often provides significantly better performance than the
Ledoit-Wolf estimator and has the advantage that consistency is guaranteed over
the whole class of elliptical distributions with finite 4th order moments.
