  We consider the estimation of the covariance of a stationary Gaussian process
on a multi-dimensional grid from observations taken on a general acquisition
domain. We derive spectral-norm risk rates for multi-taper estimators. When
applied to one dimensional acquisition intervals, these show that Thomson's
classical multi-taper has optimal risk rates, as they match known benchmarks.
We also extend existing lower risk bounds to multi-dimensional grids and
conclude that multi-taper estimators associated with certain two-dimensional
acquisition domains also have almost optimal risk rates.
