Before revision:  The obtained non-parametric estimator for the high-dimensional mean vector has a simple structure and is proven to minimize asymptotically  with probability 1  the quadratic loss in the case of c\in(0,1).
After revision:  The obtained non-parametric estimator for the high-dimensional mean vector has a simple structure and is proven to minimize asymptotically with probability 1 the quadratic loss when c\in(0,1).