[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v79y2023i4p3332-3344.html
   My bibliography  Save this article

Homogeneity tests of covariance for high‐dimensional functional data with applications to event segmentation

Author

Listed:
  • Ping‐Shou Zhong
Abstract
We consider inference problems for high‐dimensional (HD) functional data with a dense number of T repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal dependence, high dimensionality, and dense number of repeated measurements pose theoretical and computational challenges. This paper has two aims; our first aim is to solve the theoretical and computational challenges in testing equivalence among covariance matrices from HD functional data. The second aim is to provide computationally efficient and tuning‐free tools with guaranteed stochastic error control. The weak convergence of the stochastic process formed by the test statistics is established under the “large p, large T, and small n” setting. If the null is rejected, we further show that the locations of the change points can be estimated consistently. The estimator's rate of convergence is shown to depend on the data dimension, sample size, number of repeated measurements, and signal‐to‐noise ratio. We also show that our proposed computation algorithms can significantly reduce the computation time and are applicable to real‐world data with a large number of HD‐repeated measurements (e.g., functional magnetic resonance imaging (fMRI) data). Simulation results demonstrate both the finite sample performance and computational effectiveness of our proposed procedures. We observe that the empirical size of the test is well controlled at the nominal level, and the locations of multiple change points can be accurately identified. An application to fMRI data demonstrates that our proposed methods can identify event boundaries in the preface of the television series Sherlock. Code to implement the procedures is available in an R package named TechPhD.

Suggested Citation

  • Ping‐Shou Zhong, 2023. "Homogeneity tests of covariance for high‐dimensional functional data with applications to event segmentation," Biometrics, The International Biometric Society, vol. 79(4), pages 3332-3344, December.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:4:p:3332-3344
    DOI: 10.1111/biom.13844
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13844
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13844?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. Qing Yang & Guangming Pan, 2017. "Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 188-200, January.
    2. Minya Xu & Ping-Shou Zhong & Wei Wang, 2016. "Detecting Variance Change-Points for Blocked Time Series and Dependent Panel Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 213-226, April.
    3. Juhl, Ted & Xiao, Zhijie, 2009. "Tests for changing mean with monotonic power," Journal of Econometrics, Elsevier, vol. 148(1), pages 14-24, January.
    4. Ping‐Shou Zhong & Jun Li & Piotr Kokoszka, 2021. "Multivariate analysis of variance and change points estimation for high‐dimensional longitudinal data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 375-405, June.
    5. 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.
    6. Srivastava, Muni S. & Yanagihara, Hirokazu, 2010. "Testing the equality of several covariance matrices with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1319-1329, July.
    7. Jun Li, 2020. "Asymptotic distribution-free change-point detection based on interpoint distances for high-dimensional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 32(1), pages 157-184, January.
    8. David S. Matteson & Nicholas A. James, 2014. "A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 334-345, March.
    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. 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.
    2. Tsukuda, Koji & Matsuura, Shun, 2019. "High-dimensional testing for proportional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 412-420.
    3. Ke-Hai Yuan & Yubin Tian & Hirokazu Yanagihara, 2015. "Empirical Correction to the Likelihood Ratio Statistic for Structural Equation Modeling with Many Variables," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 379-405, June.
    4. Tao Zhang & Zhiwen Wang & Yanling Wan, 2021. "Functional test for high-dimensional covariance matrix, with application to mitochondrial calcium concentration," Statistical Papers, Springer, vol. 62(3), pages 1213-1230, June.
    5. Dörnemann, Nina, 2023. "Likelihood ratio tests under model misspecification in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    6. Angulo, Ana & Burridge, Peter & Mur, Jesús, 2018. "Testing for breaks in the weighting matrix," Regional Science and Urban Economics, Elsevier, vol. 68(C), pages 115-129.
    7. Jinyuan Chang & Wen Zhou & Wen-Xin Zhou & Lan Wang, 2017. "Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering," Biometrics, The International Biometric Society, vol. 73(1), pages 31-41, March.
    8. Peng Sun & Yincai Tang & Mingxiang Cao, 2022. "Homogeneity Test of Multi-Sample Covariance Matrices in High Dimensions," Mathematics, MDPI, vol. 10(22), pages 1-19, November.
    9. Cai, T. Tony & Zhang, Anru, 2016. "Inference for high-dimensional differential correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 107-126.
    10. Tsukuda, Koji & Matsuura, Shun, 2021. "Limit theorem associated with Wishart matrices with application to hypothesis testing for common principal components," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    11. Dette, Holger & Dörnemann, Nina, 2020. "Likelihood ratio tests for many groups in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    12. Taras Bodnar & Arjun Gupta, 2013. "An exact test for a column of the covariance matrix based on a single observation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(6), pages 847-855, August.
    13. Harrar, Solomon W. & Kong, Xiaoli, 2016. "High-dimensional multivariate repeated measures analysis with unequal covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 1-21.
    14. Li, Weiming & Qin, Yingli, 2014. "Hypothesis testing for high-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 108-119.
    15. DAVID E. ALLEN & MICHAEL McALEER & ROBERT J. POWELL & ABHAY K. SINGH, 2018. "Non-Parametric Multiple Change Point Analysis Of The Global Financial Crisis," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 1-23, June.
    16. 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).
    17. Baoni Li & Lihua Xiong & Quan Zhang & Shilei Chen & Han Yang & Shuhui Guo, 2022. "Effects of land use/cover change on atmospheric humidity in three urban agglomerations in the Yangtze River Economic Belt, China," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 113(1), pages 577-613, August.
    18. Zhou, Bu & Guo, Jia, 2017. "A note on the unbiased estimator of Σ2," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 141-146.
    19. 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.
    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.

    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:biomet:v:79:y:2023:i:4:p:3332-3344. 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: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    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.