  This work addresses large dimensional covariance matrix estimation with
unknown mean. The empirical covariance estimator fails when dimension and
number of samples are proportional and tend to infinity, settings known as
Kolmogorov asymptotics. When the mean is known, Ledoit and Wolf (2004) proposed
a linear shrinkage estimator and proved its convergence under those
asymptotics. To the best of our knowledge, no formal proof has been proposed
when the mean is unknown. To address this issue, we propose a new estimator and
prove its quadratic convergence under the Ledoit and Wolf assumptions. Finally,
we show empirically that it outperforms other standard estimators.
