IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v48y2021i2p375-405.html
   My bibliography  Save this article

Multivariate analysis of variance and change points estimation for high‐dimensional longitudinal data

Author

Listed:
  • Ping‐Shou Zhong
  • Jun Li
  • Piotr Kokoszka

Abstract

This article considers the problem of testing temporal homogeneity of p‐dimensional population mean vectors from repeated measurements on n subjects over T times. To cope with the challenges brought about by high‐dimensional longitudinal data, we propose methodology that takes into account not only the “large p, large T, and small n” situation but also the complex temporospatial dependence. We consider both the multivariate analysis of variance problem and the change point problem. The asymptotic distributions of the proposed test statistics are established under mild conditions. In the change point setting, when the null hypothesis of temporal homogeneity is rejected, we further propose a binary segmentation method and show that it is consistent with a rate that explicitly depends on p,T, and n. Simulation studies and an application to fMRI data are provided to demonstrate the performance and applicability of the proposed methods.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:48:y:2021:i:2:p:375-405
    DOI: 10.1111/sjos.12460
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/sjos.12460
    Download Restriction: no
    File URL: https://libkey.io/10.1111/sjos.12460?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. Haeran Cho & Piotr Fryzlewicz, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 475-507, March.
    2. Cho, Haeran & Fryzlewicz, Piotr, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," LSE Research Online Documents on Economics 57147, London School of Economics and Political Science, LSE Library.
    3. Tengyao Wang & Richard J. Samworth, 2018. "High dimensional change point estimation via sparse projection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(1), pages 57-83, January.
    4. Srivastava, Muni S. & Kubokawa, Tatsuya, 2013. "Tests for multivariate analysis of variance in high dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 204-216.
    5. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    6. Jiang Hu & Zhidong Bai & Chen Wang & Wei Wang, 2017. "On testing the equality of high dimensional mean vectors with unequal covariance matrices," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 365-387, April.
    7. Russell Epstein & Nancy Kanwisher, 1998. "A cortical representation of the local visual environment," Nature, Nature, vol. 392(6676), pages 598-601, April.
    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. Natalie Neumeyer & Miguel A. Delgado & Lajos Horváth & Simos Meintanis & Emanuele Taufer & Lixing Zhu, 2021. "4th Workshop on Goodness‐of‐Fit, Change‐Point, and Related Problems, Trento, 2019," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 371-374, June.
    2. 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.

    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. Liu, Bin & Zhang, Xinsheng & Liu, Yufeng, 2022. "High dimensional change point inference: Recent developments and extensions," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Steland, Ansgar, 2020. "Testing and estimating change-points in the covariance matrix of a high-dimensional time series," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    3. Li, Degui, 2024. "Estimation of Large Dynamic Covariance Matrices: A Selective Review," Econometrics and Statistics, Elsevier, vol. 29(C), pages 16-30.
    4. Fryzlewicz, Piotr, 2020. "Detecting possibly frequent change-points: Wild Binary Segmentation 2 and steepest-drop model selection," LSE Research Online Documents on Economics 103430, London School of Economics and Political Science, LSE Library.
    5. Jamshid Namdari & Debashis Paul & Lili Wang, 2021. "High-Dimensional Linear Models: A Random Matrix Perspective," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 645-695, August.
    6. Chen, Likai & Wang, Weining & Wu, Wei Biao, 2019. "Inference of Break-Points in High-Dimensional Time Series," IRTG 1792 Discussion Papers 2019-013, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    7. Cui, Junfeng & Wang, Guanghui & Zou, Changliang & Wang, Zhaojun, 2023. "Change-point testing for parallel data sets with FDR control," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    8. Cho, Haeran & Korkas, Karolos K., 2022. "High-dimensional GARCH process segmentation with an application to Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 23(C), pages 187-203.
    9. Cho, Haeran & Kirch, Claudia, 2024. "Data segmentation algorithms: Univariate mean change and beyond," Econometrics and Statistics, Elsevier, vol. 30(C), pages 76-95.
    10. Zhang, Jin-Ting & Zhou, Bu & Guo, Jia, 2022. "Linear hypothesis testing in high-dimensional heteroscedastic one-way MANOVA: A normal reference L2-norm based test," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    11. Zhang, Qiuyan & Wang, Chen & Zhang, Baoxue & Yang, Hu, 2024. "An RIHT statistic for testing the equality of several high-dimensional mean vectors under homoskedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).
    12. Bin Liu & Cheng Zhou & Xinsheng Zhang & Yufeng Liu, 2020. "A unified data‐adaptive framework for high dimensional change point detection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(4), pages 933-963, September.
    13. Harrar, Solomon W. & Kong, Xiaoli, 2022. "Recent developments in high-dimensional inference for multivariate data: Parametric, semiparametric and nonparametric approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    14. Pang, Tianxiao & Du, Lingjie & Chong, Terence Tai-Leung, 2021. "Estimating multiple breaks in nonstationary autoregressive models," Journal of Econometrics, Elsevier, vol. 221(1), pages 277-311.
    15. Jin-Ting Zhang & Bu Zhou & Jia Guo, 2022. "Testing high-dimensional mean vector with applications," Statistical Papers, Springer, vol. 63(4), pages 1105-1137, August.
    16. Aaron Paul Lowther & Rebecca Killick & Idris Arthur Eckley, 2023. "Detecting changes in mixed‐sampling rate data sequences," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    17. Mengjia Yu & Xiaohui Chen, 2021. "Finite sample change point inference and identification for high‐dimensional mean vectors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 247-270, April.
    18. Hajra Siddiqa & Sajid Ali & Ismail Shah, 2021. "Most recent changepoint detection in censored panel data," Computational Statistics, Springer, vol. 36(1), pages 515-540, March.
    19. Barigozzi, Matteo & Cho, Haeran & Fryzlewicz, Piotr, 2018. "Simultaneous multiple change-point and factor analysis for high-dimensional time series," Journal of Econometrics, Elsevier, vol. 206(1), pages 187-225.
    20. Chen, Cathy Yi-hsuan & Okhrin, Yarema & Wang, Tengyao, 2022. "Monitoring network changes in social media," LSE Research Online Documents on Economics 113742, London School of Economics and Political Science, LSE Library.

    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:scjsta:v:48:y:2021:i:2:p:375-405. 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=0303-6898 .

    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.