IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i10p2554-2570.html
   My bibliography  Save this article

A new test for sphericity of the covariance matrix for high dimensional data

Author

Listed:
  • Fisher, Thomas J.
  • Sun, Xiaoqian
  • Gallagher, Colin M.

Abstract

In this paper we propose a new test procedure for sphericity of the covariance matrix when the dimensionality, p, exceeds that of the sample size, N=n+1. Under the assumptions that (A) as p-->[infinity] for i=1,...,16 and (B) p/n-->c [infinity]. Our simulation results show that the new test is comparable to, and in some cases more powerful than, the tests for sphericity in the current literature.

Suggested Citation

  • Fisher, Thomas J. & Sun, Xiaoqian & Gallagher, Colin M., 2010. "A new test for sphericity of the covariance matrix for high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2554-2570, November.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2554-2570
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00151-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. C. R. Narayanaswamy & D. Raghavarao, 1991. "Principal Component Analysis of Large Dispersion Matrices," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(2), pages 309-316, June.
    2. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
    3. James R. Schott, 2005. "Testing for complete independence in high dimensions," Biometrika, Biometrika Trust, vol. 92(4), pages 951-956, December.
    4. Schott, James R., 2007. "A test for the equality of covariance matrices when the dimension is large relative to the sample sizes," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6535-6542, August.
    5. Schott, James R., 2006. "A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 827-843, April.
    6. Saranadasa, H., 1993. "Asymptotic Expansion of the Misclassification Probabilities of D- and A-Criteria for Discrimination from Two High Dimensional Populations Using the Theory of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 46(1), pages 154-174, July.
    7. Yin, Y. Q. & Krishnaiah, P. R., 1983. "A limit theorem for the eigenvalues of product of two random matrices," Journal of Multivariate Analysis, Elsevier, vol. 13(4), pages 489-507, December.
    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. Gupta, Arjun K. & Bodnar, Taras, 2014. "An exact test about the covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 176-189.
    2. Wang, Zhendong & Xu, Xingzhong, 2021. "Testing high dimensional covariance matrices via posterior Bayes factor," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    3. Wang, Cheng & Yang, Jing & Miao, Baiqi & Cao, Longbing, 2013. "Identity tests for high dimensional data using RMT," Journal of Multivariate Analysis, Elsevier, vol. 118(C), pages 128-137.
    4. Tian, Xintao & Lu, Yuting & Li, Weiming, 2015. "A robust test for sphericity of high-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 217-227.
    5. Qin, Yingli & Li, Weiming, 2016. "Testing the order of a population spectral distribution for high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 75-82.
    6. Wang, Xuanci & Zhang, Bin, 2024. "Target selection in shrinkage estimation of covariance matrix: A structural similarity approach," Statistics & Probability Letters, Elsevier, vol. 208(C).
    7. Zhang, Xiaoxu & Zhao, Ping & Feng, Long, 2022. "Robust sphericity test in the panel data model," Statistics & Probability Letters, Elsevier, vol. 182(C).
    8. Liu, Baisen & Xu, Lin & Zheng, Shurong & Tian, Guo-Liang, 2014. "A new test for the proportionality of two large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 293-308.
    9. Butucea, Cristina & Zgheib, Rania, 2016. "Sharp minimax tests for large Toeplitz covariance matrices with repeated observations," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 164-176.
    10. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    11. Deepak Nag Ayyala & Santu Ghosh & Daniel F. Linder, 2022. "Covariance matrix testing in high dimension using random projections," Computational Statistics, Springer, vol. 37(3), pages 1111-1141, July.
    12. Mao, Guangyu, 2014. "A note on tests of sphericity and cross-sectional dependence for fixed effects panel model," Economics Letters, Elsevier, vol. 122(2), pages 215-219.
    13. Glombek, Konstantin, 2013. "A Jarque-Bera test for sphericity of a large-dimensional covariance matrix," Discussion Papers in Econometrics and Statistics 1/13, University of Cologne, Institute of Econometrics and Statistics.
    14. Zhendong Wang & Xingzhong Xu, 2021. "High-dimensional sphericity test by extended likelihood ratio," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1169-1212, November.
    15. Qian, Manling & Tao, Li & Li, Erqian & Tian, Maozai, 2020. "Hypothesis testing for the identity of high-dimensional covariance matrices," Statistics & Probability Letters, Elsevier, vol. 161(C).
    16. Bodnar, Taras & Dette, Holger & Parolya, Nestor, 2019. "Testing for independence of large dimensional vectors," MPRA Paper 97997, University Library of Munich, Germany, revised May 2019.

    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. Mingyue Hu & Yongcheng Qi, 2023. "Limiting distributions of the likelihood ratio test statistics for independence of normal random vectors," Statistical Papers, Springer, vol. 64(3), pages 923-954, June.
    2. Srivastava, Muni S. & Reid, N., 2012. "Testing the structure of the covariance matrix with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 156-171.
    3. Srivastava, Muni S., 2006. "Minimum distance classification rules for high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 2057-2070, October.
    4. Yongcheng Qi & Fang Wang & Lin Zhang, 2019. "Limiting distributions of likelihood ratio test for independence of components for high-dimensional normal vectors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 911-946, August.
    5. Makoto Aoshima & Kazuyoshi Yata, 2014. "A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 983-1010, October.
    6. Tiefeng Jiang & Yongcheng Qi, 2015. "Likelihood Ratio Tests for High-Dimensional Normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 988-1009, December.
    7. Schott, James R., 2007. "A test for the equality of covariance matrices when the dimension is large relative to the sample sizes," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6535-6542, August.
    8. Xu, Kai & Hao, Xinxin, 2019. "A nonparametric test for block-diagonal covariance structure in high dimension and small samples," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 551-567.
    9. Long Feng & Changliang Zou & Zhaojun Wang, 2016. "Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 721-735, April.
    10. Jiayu Lai & Xiaoyi Wang & Kaige Zhao & Shurong Zheng, 2023. "Block-diagonal test for high-dimensional covariance matrices," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 447-466, March.
    11. Merlevède, F. & Peligrad, M., 2016. "On the empirical spectral distribution for matrices with long memory and independent rows," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2734-2760.
    12. Kubokawa, Tatsuya & Srivastava, Muni S., 2008. "Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1906-1928, October.
    13. Zhang, Yangchun & Zhou, Yirui & Liu, Xiaowei, 2023. "Applications on linear spectral statistics of high-dimensional sample covariance matrix with divergent spectrum," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    14. Hossain, Ahmed & Beyene, Joseph & Willan, Andrew R. & Hu, Pingzhao, 2009. "A flexible approximate likelihood ratio test for detecting differential expression in microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3685-3695, August.
    15. Luca Scrucca, 2014. "Graphical tools for model-based mixture discriminant analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(2), pages 147-165, June.
    16. Wang, Cheng, 2014. "Asymptotic power of likelihood ratio tests for high dimensional data," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 184-189.
    17. Bilin Zeng & Xuerong Meggie Wen & Lixing Zhu, 2017. "A link-free sparse group variable selection method for single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2388-2400, October.
    18. 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.
    19. J. Burez & D. Van Den Poel, 2005. "CRM at a Pay-TV Company: Using Analytical Models to Reduce Customer Attrition by Targeted Marketing for Subscription Services," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 05/348, Ghent University, Faculty of Economics and Business Administration.
    20. Wessel N. van Wieringen & Carel F. W. Peeters & Renee X. de Menezes & Mark A. van de Wiel, 2018. "Testing for pathway (in)activation by using Gaussian graphical models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1419-1436, November.

    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:101:y:2010:i:10:p:2554-2570. 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.