Bernoulli

  • Bernoulli
  • Volume 26, Number 1 (2020), 387-417.

High dimensional deformed rectangular matrices with applications in matrix denoising

Xiucai Ding

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Abstract

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.

Article information

Source
Bernoulli, Volume 26, Number 1 (2020), 387-417.

Dates
Received: August 2017
Revised: November 2018
First available in Project Euclid: 26 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.bj/1574758832

Digital Object Identifier
doi:10.3150/19-BEJ1129

Mathematical Reviews number (MathSciNet)
MR4036038

Zentralblatt MATH identifier
07140503

Keywords
matrix denoising random matrices rotation invariant estimation singular value decomposition

Citation

Ding, Xiucai. High dimensional deformed rectangular matrices with applications in matrix denoising. Bernoulli 26 (2020), no. 1, 387--417. doi:10.3150/19-BEJ1129. https://projecteuclid.org/euclid.bj/1574758832


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Supplemental materials

  • Supplement to “High dimensional deformed rectangular matrices with applications in matrix denoising”. This supplementary material contains auxiliary lemmas and proofs of Proposition 3.3, Theorems 3.4 and 3.5, Lemmas 4.4, 4.6, 4.8, 5.3, 5.5 and 5.6.