IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v184y2022ics0167715222000098.html
   My bibliography  Save this article

Robust sparse precision matrix estimation for high-dimensional compositional data

Author

Listed:
  • Liang, Wanfeng
  • Wu, Yue
  • Ma, Xiaoyan

Abstract

Motivated by the rapid development in the high-dimensional compositional data analysis, an ”Approximate-Plug” framework with theoretical justifications is proposed to provide robust precision matrix estimation for this kind of data under the sparsity assumption. To be specific, we first construct a Huber-robustness estimator Γ̃ to approximate the centered log-ratio covariance matrix. Then we plug Γ̃ into a constrained ℓ1-minimization procedure to obtain the final estimator Ω̃. Through imposing some mild conditions, we derive the convergence rate under the entrywise maximum norm and the spectral norm. Given that SpiecEasi in Kurtz et al. (2015) shares same routine with us but lacks of robustness and theoretical guarantees, simulation studies are conducted to show the privileges of our procedure. We also apply the proposed method on a real data.

Suggested Citation

  • Liang, Wanfeng & Wu, Yue & Ma, Xiaoyan, 2022. "Robust sparse precision matrix estimation for high-dimensional compositional data," Statistics & Probability Letters, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:stapro:v:184:y:2022:i:c:s0167715222000098
    DOI: 10.1016/j.spl.2022.109379
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715222000098
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2022.109379?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Banerjee, Sayantan & Ghosal, Subhashis, 2015. "Bayesian structure learning in graphical models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 147-162.
    2. Wang, Luheng & Chen, Zhao & Wang, Christina Dan & Li, Runze, 2020. "Ultrahigh dimensional precision matrix estimation via refitted cross validation," Journal of Econometrics, Elsevier, vol. 215(1), pages 118-130.
    3. Lam, Clifford & Fan, Jianqing, 2009. "Sparsistency and rates of convergence in large covariance matrix estimation," LSE Research Online Documents on Economics 31540, London School of Economics and Political Science, LSE Library.
    4. 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.
    5. 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.
    6. Jianhua Z. Huang & Naiping Liu & Mohsen Pourahmadi & Linxu Liu, 2006. "Covariance matrix selection and estimation via penalised normal likelihood," Biometrika, Biometrika Trust, vol. 93(1), pages 85-98, March.
    7. J. L. Scealy & Patrice de Caritat & Eric C. Grunsky & Michail T. Tsagris & A. H. Welsh, 2015. "Robust Principal Component Analysis for Power Transformed Compositional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 136-148, March.
    8. 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.
    9. Adam J. Rothman & Elizaveta Levina & Ji Zhu, 2010. "A new approach to Cholesky-based covariance regularization in high dimensions," Biometrika, Biometrika Trust, vol. 97(3), pages 539-550.
    10. Qiang Sun & Wen-Xin Zhou & Jianqing Fan, 2020. "Adaptive Huber Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 254-265, January.
    11. Cai, Tony & Liu, Weidong & Luo, Xi, 2011. "A Constrained â„“1 Minimization Approach to Sparse Precision Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 594-607.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Luheng & Chen, Zhao & Wang, Christina Dan & Li, Runze, 2020. "Ultrahigh dimensional precision matrix estimation via refitted cross validation," Journal of Econometrics, Elsevier, vol. 215(1), pages 118-130.
    2. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    3. Bailey, Natalia & Pesaran, M. Hashem & Smith, L. Vanessa, 2019. "A multiple testing approach to the regularisation of large sample correlation matrices," Journal of Econometrics, Elsevier, vol. 208(2), pages 507-534.
    4. Ines Wilms & Jacob Bien, 2021. "Tree-based Node Aggregation in Sparse Graphical Models," Papers 2101.12503, arXiv.org.
    5. Yumou Qiu & Song Xi Chen, 2015. "Bandwidth Selection for High-Dimensional Covariance Matrix Estimation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1160-1174, September.
    6. Cao, Xuan & Khare, Kshitij & Ghosh, Malay, 2020. "Consistent Bayesian sparsity selection for high-dimensional Gaussian DAG models with multiplicative and beta-mixture priors," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    7. Xingqi Du & Subhashis Ghosal, 2018. "Bayesian Discriminant Analysis Using a High Dimensional Predictor," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 112-145, December.
    8. Banerjee, Sayantan & Ghosal, Subhashis, 2015. "Bayesian structure learning in graphical models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 147-162.
    9. Benjamin Poignard & Manabu Asai, 2023. "Estimation of high-dimensional vector autoregression via sparse precision matrix," The Econometrics Journal, Royal Economic Society, vol. 26(2), pages 307-326.
    10. Kang, Xiaoning & Wang, Mingqiu, 2021. "Ensemble sparse estimation of covariance structure for exploring genetic disease data," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    11. Fang, Qian & Yu, Chen & Weiping, Zhang, 2020. "Regularized estimation of precision matrix for high-dimensional multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    12. Xue, Lingzhou & Zou, Hui, 2013. "Minimax optimal estimation of general bandable covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 45-51.
    13. McGillivray, Annaliza & Khalili, Abbas & Stephens, David A., 2020. "Estimating sparse networks with hubs," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    14. Luo, Shan & Chen, Zehua, 2014. "Edge detection in sparse Gaussian graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 138-152.
    15. Qiu, Yumou & Chen, Songxi, 2012. "Test for Bandedness of High Dimensional Covariance Matrices with Bandwidth Estimation," MPRA Paper 46242, University Library of Munich, Germany.
    16. Ruijun Bu & Degui Li & Oliver Linton & Hanchao Wang, 2022. "Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data," Working Papers 202212, University of Liverpool, Department of Economics.
    17. Pei Wang & Shunjie Chen & Sijia Yang, 2022. "Recent Advances on Penalized Regression Models for Biological Data," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    18. Wei Lan & Ronghua Luo & Chih-Ling Tsai & Hansheng Wang & Yunhong Yang, 2015. "Testing the Diagonality of a Large Covariance Matrix in a Regression Setting," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 76-86, January.
    19. Guanghui Cheng & Zhengjun Zhang & Baoxue Zhang, 2017. "Test for bandedness of high-dimensional precision matrices," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 884-902, October.
    20. Gautam Sabnis & Debdeep Pati & Anirban Bhattacharya, 2019. "Compressed Covariance Estimation with Automated Dimension Learning," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 466-481, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:184:y:2022:i:c:s0167715222000098. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.