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Lower bounds for invariant statistical models with applications to principal component analysis
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.Comment: 42 pages, to appear in Annales de l'Institut Henri Poincar\'e
Probabilit\'es et Statistique
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