  We elucidate the problem of estimating large-dimensional covariance matrices
in the presence of correlations between samples. To this end, we generalize the
Marcenko-Pastur equation and the Ledoit-Peche shrinkage estimator using methods
of random matrix theory and free probability. We develop an efficient algorithm
that implements the corresponding analytic formulas, based on the Ledoit-Wolf
kernel estimation technique. We also provide an associated open-source Python
library, called "shrinkage", with a user-friendly API to assist in practical
tasks of estimation of large covariance matrices. We present an example of its
usage for synthetic data generated according to exponentially-decaying
auto-correlations.
