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Robust Principal Component Analysis with Non-Sparse Errors

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  • Jushan Bai
  • Junlong Feng

Abstract

We show that when a high-dimensional data matrix is the sum of a low-rank matrix and a random error matrix with independent entries, the low-rank component can be consistently estimated by solving a convex minimization problem. We develop a new theoretical argument to establish consistency without assuming sparsity or the existence of any moments of the error matrix, so that fat-tailed continuous random errors such as Cauchy are allowed. The results are illustrated by simulations.

Suggested Citation

  • Jushan Bai & Junlong Feng, 2019. "Robust Principal Component Analysis with Non-Sparse Errors," Papers 1902.08735, arXiv.org, revised Nov 2019.
    • Handle: RePEc:arx:papers:1902.08735
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    File URL: http://arxiv.org/pdf/1902.08735
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    Cited by:

    1. Alexandre Belloni & Mingli Chen & Oscar Hernan Madrid Padilla & Zixuan & Wang, 2019. "High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing," Papers 1912.02151, arXiv.org, revised Aug 2022.
    2. A. H. Bentbib & A. El Hachimi & K. Jbilou & A. Ratnani, 2022. "A Tensor Regularized Nuclear Norm Method for Image and Video Completion," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 401-425, February.
    3. Sedigheh Mohamadi & Saad Sh. Sammen & Fatemeh Panahi & Mohammad Ehteram & Ozgur Kisi & Amir Mosavi & Ali Najah Ahmed & Ahmed El-Shafie & Nadhir Al-Ansari, 2020. "Zoning map for drought prediction using integrated machine learning models with a nomadic people optimization algorithm," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 104(1), pages 537-579, October.
    4. Trucíos, Carlos & Mazzeu, João H.G. & Hotta, Luiz K. & Valls Pereira, Pedro L. & Hallin, Marc, 2021. "Robustness and the general dynamic factor model with infinite-dimensional space: Identification, estimation, and forecasting," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1520-1534.

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