Lower bounds for invariant statistical models with applications to principal component analysis
Statistics Theory
2021-07-20 v2 Information Theory
math.IT
Statistics Theory
Abstract
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.
Cite
@article{arxiv.2005.06869,
title = {Lower bounds for invariant statistical models with applications to principal component analysis},
author = {Martin Wahl},
journal= {arXiv preprint arXiv:2005.06869},
year = {2021}
}
Comments
42 pages, to appear in Annales de l'Institut Henri Poincar\'e Probabilit\'es et Statistiques