This paper develops nonasymptotic information inequalities for the estimation of the eigenspaces of a covariance operator. These results generalize previous lower bounds for the spiked covariance model, and they show that recent upper bounds for models with decaying eigenvalues are sharp. The proof relies on lower bound techniques based on group invariance arguments which can also deal with a variety of other statistical models.

翻译：本文为估算一个共变操作器的源空开发了非隐性信息不平等性。 这些结果概括了加压共变模型以前的下限,并表明,与衰减的源值有关的模型最近的上限是锐利的。 证据依据基于群集异性参数的较低约束技术,这些参数也可以处理其他各种统计模型。