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Sparse basis covariance matrix estimation for high dimensional compositional data via hard thresholding

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  • Li, Huimin
  • Wang, Jinru

Abstract

Motivated by the high-dimensional compositional data appearing in many fields, this paper addresses the problem of large covariance estimation for compositional data. Firstly, we introduce the hard thresholding estimator to approximate the sparse basis covariance matrix which is relevant with compositional data. Then the upper error bounds are measured by the general matrix lv,w-norm and the general entrywise Lv,w-norm respectively with v,w∈[1,∞] in terms of probability. Finally, numerical simulations and real datasets application demonstrate that our estimator is close to the oracle estimator and outperforms the COAT estimator proposed by Cao et al. (2019).

Suggested Citation

  • Li, Huimin & Wang, Jinru, 2024. "Sparse basis covariance matrix estimation for high dimensional compositional data via hard thresholding," Statistics & Probability Letters, Elsevier, vol. 209(C).
    • Handle: RePEc:eee:stapro:v:209:y:2024:i:c:s0167715224000579
    DOI: 10.1016/j.spl.2024.110088
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    References listed on IDEAS

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    1. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    2. Zhang, Qihu & Park, Cheolwoo & Chung, Jongik, 2021. "Minimax estimation of covariance and precision matrices for high-dimensional time series with long-memory," Statistics & Probability Letters, Elsevier, vol. 177(C).
    3. Adam J. Rothman, 2012. "Positive definite estimators of large covariance matrices," Biometrika, Biometrika Trust, vol. 99(3), pages 733-740.
    4. Peter J. Turnbaugh & Micah Hamady & Tanya Yatsunenko & Brandi L. Cantarel & Alexis Duncan & Ruth E. Ley & Mitchell L. Sogin & William J. Jones & Bruce A. Roe & Jason P. Affourtit & Michael Egholm & Be, 2009. "A core gut microbiome in obese and lean twins," Nature, Nature, vol. 457(7228), pages 480-484, January.
    5. Yuanpei Cao & Wei Lin & Hongzhe Li, 2019. "Large Covariance Estimation for Compositional Data Via Composition-Adjusted Thresholding," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 759-772, April.
    6. Zachary D Kurtz & Christian L Müller & Emily R Miraldi & Dan R Littman & Martin J Blaser & Richard A Bonneau, 2015. "Sparse and Compositionally Robust Inference of Microbial Ecological Networks," PLOS Computational Biology, Public Library of Science, vol. 11(5), pages 1-25, May.
    7. Marco Avella-Medina & Heather S Battey & Jianqing Fan & Quefeng Li, 2018. "Robust estimation of high-dimensional covariance and precision matrices," Biometrika, Biometrika Trust, vol. 105(2), pages 271-284.
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