IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v169y2019icp21-32.html
   My bibliography  Save this article

Projection tests for high-dimensional spiked covariance matrices

Author

Listed:
  • Guo, Wenwen
  • Cui, Hengjian

Abstract

Testing the existence of low-dimensional perturbations or signals is very important, e.g., in factor analysis and signal processing. This paper aims to develop new tests for high-dimensional spiked covariance matrices based on a projection approach. The asymptotic distribution of the proposed tests is obtained under regularity conditions. We further explore a power enhancement technique under covariance matrix sparsity. The finite-sample enhanced power performance of the proposed tests is shown through simulations. A microarray dataset is used for illustration purposes.

Suggested Citation

  • Guo, Wenwen & Cui, Hengjian, 2019. "Projection tests for high-dimensional spiked covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 21-32.
  • Handle: RePEc:eee:jmvana:v:169:y:2019:i:c:p:21-32
    DOI: 10.1016/j.jmva.2018.08.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X17307558
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmva.2018.08.009?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

    for a different version of it.

    References listed on IDEAS

    as
    1. I. M. Johnstone & B. Nadler, 2017. "Roy’s largest root test under rank-one alternatives," Biometrika, Biometrika Trust, vol. 104(1), pages 181-193.
    2. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    3. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    4. 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.
    5. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    6. Jianqing Fan & Yuan Liao & Jiawei Yao, 2015. "Power Enhancement in High‐Dimensional Cross‐Sectional Tests," Econometrica, Econometric Society, vol. 83(4), pages 1497-1541, July.
    7. Meinshausen, Nicolai & Meier, Lukas & Bühlmann, Peter, 2009. "p-Values for High-Dimensional Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1671-1681.
    8. Chen, Songxi, 2012. "Two Sample Tests for High Dimensional Covariance Matrices," MPRA Paper 46026, University Library of Munich, Germany.
    9. Peng, Liuhua & Chen, Song Xi & Zhou, Wen, 2016. "More powerful tests for sparse high-dimensional covariances matrices," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 124-143.
    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. Congran Yu & Hengjian Cui, 2025. "Feature screening via false discovery rate control for linear model with multivariate responses," Statistical Papers, Springer, vol. 66(2), pages 1-29, February.

    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. Yanpeng, Li & Jiahui, Xie & Guoliang, Zhou & Wang, Zhou, 2025. "Sequential estimation of high-dimensional signal plus noise models under general elliptical frameworks," Journal of Multivariate Analysis, Elsevier, vol. 207(C).
    2. Bodnar, Taras & Reiß, Markus, 2016. "Exact and asymptotic tests on a factor model in low and large dimensions with applications," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 125-151.
    3. 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.
    4. Jianqing Fan & Kunpeng Li & Yuan Liao, 2020. "Recent Developments on Factor Models and its Applications in Econometric Learning," Papers 2009.10103, arXiv.org.
    5. Alain-Philippe Fortin & Patrick Gagliardini & O. Scaillet, 2022. "Eigenvalue tests for the number of latent factors in short panels," Swiss Finance Institute Research Paper Series 22-81, Swiss Finance Institute.
    6. Fan, Jianqing & Liao, Yuan & Shi, Xiaofeng, 2015. "Risks of large portfolios," Journal of Econometrics, Elsevier, vol. 186(2), pages 367-387.
    7. Chen, Liang, 2012. "Identifying observed factors in approximate factor models: estimation and hypothesis testing," MPRA Paper 37514, University Library of Munich, Germany.
    8. Wang, Cheng, 2014. "Asymptotic power of likelihood ratio tests for high dimensional data," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 184-189.
    9. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    10. Bai, Jushan & Duan, Jiangtao & Han, Xu, 2024. "The likelihood ratio test for structural changes in factor models," Journal of Econometrics, Elsevier, vol. 238(2).
    11. Chen, Song Xi & Guo, Bin & Qiu, Yumou, 2023. "Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding," Journal of Econometrics, Elsevier, vol. 235(2), pages 1337-1354.
    12. Claudio Barbieri & Mattia Guerini & Mauro Napoletano, 2021. "The anatomy of government bond yields synchronization in the Eurozone," SciencePo Working papers Main hal-03373853, HAL.
    13. Charles Olivier Mao Takongmo & Dalibor Stevanovic, 2015. "Selection Of The Number Of Factors In Presence Of Structural Instability: A Monte Carlo Study," L'Actualité Economique, Société Canadienne de Science Economique, vol. 91(1-2), pages 177-233.
    14. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    15. Forni, Mario & Hallin, Marc & Lippi, Marco & Zaffaroni, Paolo, 2017. "Dynamic factor models with infinite-dimensional factor space: Asymptotic analysis," Journal of Econometrics, Elsevier, vol. 199(1), pages 74-92.
    16. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    17. Yitian Liu & Jiazhu Pan & Qiang Xia, 2025. "Estimation of Constrained Factor Models for High‐Dimensional Time Series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 44(4), pages 1467-1477, July.
    18. Sung Hoon Choi & Donggyu Kim, 2023. "Large Global Volatility Matrix Analysis Based on Observation Structural Information," Papers 2305.01464, arXiv.org, revised Feb 2024.
    19. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    20. Barigozzi, Matteo & Hallin, Marc & Luciani, Matteo & Zaffaroni, Paolo, 2024. "Inferential theory for generalized dynamic factor models," Journal of Econometrics, Elsevier, vol. 239(2).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    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:eee:jmvana:v:169:y:2019:i:c:p:21-32. 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.