IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v103y2016i3p653-666..html
   My bibliography  Save this article

A theoretical study of Stein's covariance estimator

Author

Listed:
  • Bala Rajaratnam
  • Dario Vincenzi

Abstract

Stein proposed an estimator to address the poor performance of the sample covariance matrix for samples of small size. The estimator does not impose sparsity conditions and uses an isotonizing algorithm to preserve the order of the sample eigenvalues. Despite its superior numerical performance, its theoretical properties are not well understood. We demonstrate that Stein's covariance estimator gives modest risk reductions when it is not isotonized, and when it is isotonized the risk reductions are significant. Three broad regimes of the estimator's behaviour are identified.

Suggested Citation

  • Bala Rajaratnam & Dario Vincenzi, 2016. "A theoretical study of Stein's covariance estimator," Biometrika, Biometrika Trust, vol. 103(3), pages 653-666.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:3:p:653-666.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asw030
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Olivier Ledoit & Michael Wolf, 2017. "Analytical nonlinear shrinkage of large-dimensional covariance matrices," ECON - Working Papers 264, Department of Economics - University of Zurich, revised Nov 2018.
    2. Olivier Ledoit & Michael Wolf, 2019. "Quadratic shrinkage for large covariance matrices," ECON - Working Papers 335, Department of Economics - University of Zurich, revised Dec 2020.

    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. Hannart, Alexis & Naveau, Philippe, 2014. "Estimating high dimensional covariance matrices: A new look at the Gaussian conjugate framework," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 149-162.
    2. Jianqing Fan & Xu Han, 2017. "Estimation of the false discovery proportion with unknown dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1143-1164, September.
    3. Wang Xiaoming & Dinu Irina & Liu Wei & Yasui Yutaka, 2011. "Linear Combination Test for Hierarchical Gene Set Analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-18, March.
    4. Seunghwan Lee & Sang Cheol Kim & Donghyeon Yu, 2023. "An efficient GPU-parallel coordinate descent algorithm for sparse precision matrix estimation via scaled lasso," Computational Statistics, Springer, vol. 38(1), pages 217-242, March.
    5. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    6. Christian Bongiorno, 2020. "Bootstraps Regularize Singular Correlation Matrices," Working Papers hal-02536278, HAL.
    7. van Wieringen, Wessel N. & Stam, Koen A. & Peeters, Carel F.W. & van de Wiel, Mark A., 2020. "Updating of the Gaussian graphical model through targeted penalized estimation," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    8. Mr. Jorge A Chan-Lau, 2017. "Variance Decomposition Networks: Potential Pitfalls and a Simple Solution," IMF Working Papers 2017/107, International Monetary Fund.
    9. Boulesteix Anne-Laure, 2006. "Reader's Reaction to "Dimension Reduction for Classification with Gene Expression Microarray Data" by Dai et al (2006)," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 5(1), pages 1-7, June.
    10. Pan-Jun Kim & Nathan D Price, 2011. "Genetic Co-Occurrence Network across Sequenced Microbes," PLOS Computational Biology, Public Library of Science, vol. 7(12), pages 1-9, December.
    11. repec:hum:wpaper:sfb649dp2012-049 is not listed on IDEAS
    12. Sprangers, Olivier & Wadman, Wander & Schelter, Sebastian & de Rijke, Maarten, 2024. "Hierarchical forecasting at scale," International Journal of Forecasting, Elsevier, vol. 40(4), pages 1689-1700.
    13. Ledoit, Olivier & Wolf, Michael, 2017. "Numerical implementation of the QuEST function," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 199-223.
    14. Ata Kabán & Efstratios Palias, 2024. "A Bhattacharyya-type Conditional Error Bound for Quadratic Discriminant Analysis," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-17, December.
    15. Sumanjay Dutta & Shashi Jain, 2023. "Precision versus Shrinkage: A Comparative Analysis of Covariance Estimation Methods for Portfolio Allocation," Papers 2305.11298, arXiv.org.
    16. Marius Arend & Yizhong Yuan & M. Águila Ruiz-Sola & Nooshin Omranian & Zoran Nikoloski & Dimitris Petroutsos, 2023. "Widening the landscape of transcriptional regulation of green algal photoprotection," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    17. Kourentzes, Nikolaos & Saayman, Andrea & Jean-Pierre, Philippe & Provenzano, Davide & Sahli, Mondher & Seetaram, Neelu & Volo, Serena, 2021. "Visitor arrivals forecasts amid COVID-19: A perspective from the Africa team," Annals of Tourism Research, Elsevier, vol. 88(C).
    18. Vincent Guillemot & Andreas Bender & Anne-Laure Boulesteix, 2013. "Iterative Reconstruction of High-Dimensional Gaussian Graphical Models Based on a New Method to Estimate Partial Correlations under Constraints," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-10, April.
    19. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    20. Vilda Purutçuoğlu, 2013. "Inference of the stochastic MAPK pathway by modified diffusion bridge method," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(2), pages 415-429, March.
    21. Sahra Uygun & Cheng Peng & Melissa D Lehti-Shiu & Robert L Last & Shin-Han Shiu, 2016. "Utility and Limitations of Using Gene Expression Data to Identify Functional Associations," PLOS Computational Biology, Public Library of Science, vol. 12(12), pages 1-27, December.

    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:oup:biomet:v:103:y:2016:i:3:p:653-666.. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.