  In many astrophysical settings covariance matrices of large datasets have to
be determined empirically from a finite number of mock realisations. The
resulting noise degrades inference and precludes it completely if there are
fewer realisations than data points. This work applies a recently proposed
non-linear shrinkage estimator of covariance to a realistic example from
large-scale structure cosmology. After optimising its performance for the usage
in likelihood expressions, the shrinkage estimator yields subdominant bias and
variance comparable to that of the standard estimator with a factor $\sim 50$
less realisations. This is achieved without any prior information on the
properties of the data or the structure of the covariance matrix, at negligible
computational cost.
