Van Trees inequality, group equivariance, and estimation of principal subspaces

2021/07/19 by Martin Wahl, Wahl, Martin · 1 citation
Mathematics · #62B10 #62H25 #FOS: Mathematics #Graph theory and applications #Point processes and geometric inequalities #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2107.08723

openalex publication_date 2021/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish non-asymptotic lower bounds for the estimation of principal subspaces. As applications, we obtain new results for the excess risk of principal component analysis and the matrix denoising problem.

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• Toward an Asymptotic Efficiency Theory on Regular Parameter Manifolds

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