Spectral-norm risk rates for multi-taper estimation of Gaussian processes

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