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.

翻译：我们考虑从一般获取域的观测中从多维网格上对固定高斯进程共变量的估计。 我们为多层天顶测算者得出光谱- 北风险率。 当应用到一个维获取间隔时, 这些显示汤姆森的经典多层天体具有最佳风险率, 因为它们与已知基准相匹配。 我们还将现有的低风险界限扩大到多维网格, 并得出结论, 与某些二维获取域相关的多层天体测算者也几乎拥有最佳风险率 。