IDEAS home Printed from https://ideas.repec.org/a/bla/jorssc/v71y2022i1p119-147.html
   My bibliography  Save this article

Estimation of large block structured covariance matrices: Application to ‘multi‐omic’ approaches to study seed quality

Author

Listed:
  • M. Perrot‐Dockès
  • C. Lévy‐Leduc
  • L. Rajjou

Abstract

Motivated by an application in high‐throughput genomics and metabolomics, we propose a novel and fully data‐driven approach for estimating large block structured sparse covariance matrices in the case where the number of variables is much larger than the number of samples without limiting ourselves to block diagonal matrices. Our approach consists in approximating such a covariance matrix by the sum of a low‐rank sparse matrix and a diagonal matrix. Our methodology also can deal with matrices for which the block structure appears only if the columns and rows are permuted according to an unknown permutation. Our technique is implemented in the R package BlockCov which is available from the Comprehensive R Archive Network (CRAN) and from GitHub. In order to illustrate the statistical and numerical performance of our package some numerical experiments are provided as well as a thorough comparison with alternative methods. Finally, our approach is applied to the use of ‘multi‐omic’ approaches for studying seed quality.

Suggested Citation

  • M. Perrot‐Dockès & C. Lévy‐Leduc & L. Rajjou, 2022. "Estimation of large block structured covariance matrices: Application to ‘multi‐omic’ approaches to study seed quality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 119-147, January.
    • Handle: RePEc:bla:jorssc:v:71:y:2022:i:1:p:119-147
    DOI: 10.1111/rssc.12524
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/rssc.12524
    Download Restriction: no
    File URL: https://libkey.io/10.1111/rssc.12524?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
    ---><---

    References listed on IDEAS

    as
    1. Adam J. Rothman, 2012. "Positive definite estimators of large covariance matrices," Biometrika, Biometrika Trust, vol. 99(3), pages 733-740.
    2. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    3. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
    4. Jianqing Fan & Yuan Liao & Han Liu, 2016. "An overview of the estimation of large covariance and precision matrices," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 1-32, February.
    5. John Horn, 1965. "A rationale and test for the number of factors in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 30(2), pages 179-185, June.
    6. Lingzhou Xue & Shiqian Ma & Hui Zou, 2012. "Positive-Definite ℓ 1 -Penalized Estimation of Large Covariance Matrices," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1480-1491, December.
    7. Nickolay T. Trendafilov & Sara Fontanella & Kohei Adachi, 2017. "Sparse Exploratory Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 778-794, September.
    8. Jacob Bien & Robert J. Tibshirani, 2011. "Sparse estimation of a covariance matrix," Biometrika, Biometrika Trust, vol. 98(4), pages 807-820.
    9. Perrot-Dockès, Marie & Lévy-Leduc, Céline & Sansonnet, Laure & Chiquet, Julien, 2018. "Variable selection in multivariate linear models with high-dimensional covariance matrix estimation," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 78-97.
    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. Shaoxin Wang & Hu Yang & Chaoli Yao, 2019. "On the penalized maximum likelihood estimation of high-dimensional approximate factor model," Computational Statistics, Springer, vol. 34(2), pages 819-846, June.
    2. Yang, Yihe & Zhou, Jie & Pan, Jianxin, 2021. "Estimation and optimal structure selection of high-dimensional Toeplitz covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    3. Kashlak, Adam B., 2021. "Non-asymptotic error controlled sparse high dimensional precision matrix estimation," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    4. Bai, Jushan & Liao, Yuan, 2016. "Efficient estimation of approximate factor models via penalized maximum likelihood," Journal of Econometrics, Elsevier, vol. 191(1), pages 1-18.
    5. 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.
    6. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    7. Choi, Young-Geun & Lim, Johan & Roy, Anindya & Park, Junyong, 2019. "Fixed support positive-definite modification of covariance matrix estimators via linear shrinkage," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 234-249.
    8. Denis Belomestny & Mathias Trabs & Alexandre Tsybakov, 2017. "Sparse covariance matrix estimation in high-dimensional deconvolution," Working Papers 2017-25, Center for Research in Economics and Statistics.
    9. Maurizio Daniele & Winfried Pohlmeier & Aygul Zagidullina, 2018. "Sparse Approximate Factor Estimation for High-Dimensional Covariance Matrices," Working Paper Series of the Department of Economics, University of Konstanz 2018-07, Department of Economics, University of Konstanz.
    10. Xin Wang & Lingchen Kong & Liqun Wang & Zhaoqilin Yang, 2023. "High-Dimensional Covariance Estimation via Constrained L q -Type Regularization," Mathematics, MDPI, vol. 11(4), pages 1-20, February.
    11. Yan Zhang & Jiyuan Tao & Zhixiang Yin & Guoqiang Wang, 2022. "Improved Large Covariance Matrix Estimation Based on Efficient Convex Combination and Its Application in Portfolio Optimization," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    12. Zhonghui Zhang & Huarui Jing & Chihwa Kao, 2023. "High-Dimensional Distributionally Robust Mean-Variance Efficient Portfolio Selection," Mathematics, MDPI, vol. 11(5), pages 1-16, March.
    13. Azam Kheyri & Andriette Bekker & Mohammad Arashi, 2022. "High-Dimensional Precision Matrix Estimation through GSOS with Application in the Foreign Exchange Market," Mathematics, MDPI, vol. 10(22), pages 1-19, November.
    14. Seonghun Cho & Shota Katayama & Johan Lim & Young-Geun Choi, 2021. "Positive-definite modification of a covariance matrix by minimizing the matrix $$\ell_{\infty}$$ ℓ ∞ norm with applications to portfolio optimization," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 601-627, December.
    15. Ding, Yi & Li, Yingying & Zheng, Xinghua, 2021. "High dimensional minimum variance portfolio estimation under statistical factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 502-515.
    16. Cui, Ying & Leng, Chenlei & Sun, Defeng, 2016. "Sparse estimation of high-dimensional correlation matrices," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 390-403.
    17. Avagyan, Vahe & Nogales, Francisco J., 2015. "D-trace Precision Matrix Estimation Using Adaptive Lasso Penalties," DES - Working Papers. Statistics and Econometrics. WS 21775, Universidad Carlos III de Madrid. Departamento de Estadística.
    18. Wang, Xin & Kong, Lingchen & Wang, Liqun, 2024. "Estimation of sparse covariance matrix via non-convex regularization," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    19. Bai, Jushan & Ng, Serena, 2019. "Rank regularized estimation of approximate factor models," Journal of Econometrics, Elsevier, vol. 212(1), pages 78-96.
    20. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2019. "Cross-validated covariance estimators for high-dimensional minimum-variance portfolios," Papers 1910.13960, arXiv.org, revised Oct 2020.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jorssc:v:71:y:2022:i:1:p:119-147. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.