  Relying on recent advances in statistical estimation of covariance distances
based on random matrix theory, this article proposes an improved covariance and
precision matrix estimation for a wide family of metrics. The method is shown
to largely outperform the sample covariance matrix estimate and to compete with
state-of-the-art methods, while at the same time being computationally simpler.
Applications to linear and quadratic discriminant analyses also demonstrate
significant gains, therefore suggesting practical interest to statistical
machine learning.
