Open Access
February 2020 High dimensional deformed rectangular matrices with applications in matrix denoising
Xiucai Ding
Bernoulli 26(1): 387-417 (February 2020). DOI: 10.3150/19-BEJ1129


We consider the recovery of a low rank $M\times N$ matrix $S$ from its noisy observation $\tilde{S}$ in the high dimensional framework when $M$ is comparable to $N$. We propose two efficient estimators for $S$ under two different regimes. Our analysis relies on the local asymptotics of the eigenstructure of large dimensional rectangular matrices with finite rank perturbation. We derive the convergent limits and rates for the singular values and vectors for such matrices.


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Xiucai Ding. "High dimensional deformed rectangular matrices with applications in matrix denoising." Bernoulli 26 (1) 387 - 417, February 2020.


Received: 1 August 2017; Revised: 1 November 2018; Published: February 2020
First available in Project Euclid: 26 November 2019

zbMATH: 07140503
MathSciNet: MR4036038
Digital Object Identifier: 10.3150/19-BEJ1129

Keywords: Matrix denoising , random matrices , rotation invariant estimation , Singular value decomposition

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 1 • February 2020
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