Lower bounds for invariant statistical models with applications to principal component analysis

2020/05/14 by Martin Wahl, Wahl, Martin
Mathematics · #60B20 #62B10 #62H25 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Random Matrices and Applications #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2005.06869

openalex publication_date 2020/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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