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Optimal singular value shrinkage for operator norm loss: Extending to non-square matrices

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  • Leeb, William

Abstract

We correct a formula of Gavish and Donoho for singular value shrinkage with operator norm loss for non-square matrices. We also observe that in the classical regime, optimal shrinkage for any Schatten loss converges to the best linear predictor.

Suggested Citation

  • Leeb, William, 2022. "Optimal singular value shrinkage for operator norm loss: Extending to non-square matrices," Statistics & Probability Letters, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:stapro:v:186:y:2022:i:c:s0167715222000633
    DOI: 10.1016/j.spl.2022.109472
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    References listed on IDEAS

    as
    1. Shabalin, Andrey A. & Nobel, Andrew B., 2013. "Reconstruction of a low-rank matrix in the presence of Gaussian noise," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 67-76.
    2. Benaych-Georges, Florent & Nadakuditi, Raj Rao, 2012. "The singular values and vectors of low rank perturbations of large rectangular random matrices," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 120-135.
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