IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v99y2012i4p813-832.html
   My bibliography  Save this article

Dispersion operators and resistant second-order functional data analysis

Author

Listed:
  • David Kraus
  • Victor M. Panaretos

Abstract

Inferences related to the second-order properties of functional data, as expressed by covariance structure, can become unreliable when the data are non-Gaussian or contain unusual observations. In the functional setting, it is often difficult to identify atypical observations, as their distinguishing characteristics can be manifold but subtle. In this paper, we introduce the notion of a dispersion operator, investigate its use in probing the second-order structure of functional data, and develop a test for comparing the second-order characteristics of two functional samples that is resistant to atypical observations and departures from normality. The proposed test is a regularized M-test based on a spectrally truncated version of the Hilbert--Schmidt norm of a score operator defined via the dispersion operator. We derive the asymptotic distribution of the test statistic, investigate the behaviour of the test in a simulation study and illustrate the method on a structural biology dataset. Copyright 2012, Oxford University Press.

Suggested Citation

  • David Kraus & Victor M. Panaretos, 2012. "Dispersion operators and resistant second-order functional data analysis," Biometrika, Biometrika Trust, vol. 99(4), pages 813-832.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:4:p:813-832
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/ass037
    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.

    Citations

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


    Cited by:

    1. Boente, Graciela & Rodriguez, Daniela & Sued, Mariela, 2019. "The spatial sign covariance operator: Asymptotic results and applications," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 115-128.
    2. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.
    3. Italo R. Lima & Guanqun Cao & Nedret Billor, 2019. "Robust simultaneous inference for the mean function of functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 785-803, September.
    4. Francesca Ieva & Anna Maria Paganoni, 2020. "Component-wise outlier detection methods for robustifying multivariate functional samples," Statistical Papers, Springer, vol. 61(2), pages 595-614, April.
    5. Guangxing Wang & Sisheng Liu & Fang Han & Chong‐Zhi Di, 2023. "Robust functional principal component analysis via a functional pairwise spatial sign operator," Biometrics, The International Biometric Society, vol. 79(2), pages 1239-1253, June.
    6. Jing Zhao & Sanying Feng & Yuping Hu, 2022. "Two-Sample Hypothesis Test for Functional Data," Mathematics, MDPI, vol. 10(21), pages 1-16, November.
    7. Italo R. Lima & Guanqun Cao & Nedret Billor, 2019. "M-based simultaneous inference for the mean function of functional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 577-598, June.
    8. Tomasz Górecki & Lajos Horváth & Piotr Kokoszka, 2020. "Tests of Normality of Functional Data," International Statistical Review, International Statistical Institute, vol. 88(3), pages 677-697, December.
    9. Zhong, Rou & Liu, Shishi & Li, Haocheng & Zhang, Jingxiao, 2022. "Robust functional principal component analysis for non-Gaussian longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    10. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    11. Holger Dette & Kevin Kokot, 2022. "Detecting relevant differences in the covariance operators of functional time series: a sup-norm approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 195-231, April.
    12. Aaron, Catherine & Cholaquidis, Alejandro & Fraiman, Ricardo & Ghattas, Badih, 2019. "Multivariate and functional robust fusion methods for structured Big Data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 149-161.
    13. Valentina Masarotto & Victor M. Panaretos & Yoav Zemel, 2019. "Procrustes Metrics on Covariance Operators and Optimal Transportation of Gaussian Processes," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 172-213, February.
    14. Hervé Cardot & Antoine Godichon-Baggioni, 2017. "Fast estimation of the median covariation matrix with application to online robust principal components analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 461-480, September.
    15. Kokoszka Piotr & Miao Hong & Zheng Ben, 2017. "Testing for asymmetry in betas of cumulative returns: Impact of the financial crisis and crude oil price," Statistics & Risk Modeling, De Gruyter, vol. 34(1-2), pages 33-53, June.
    16. Bali, Juan Lucas & Boente, Graciela, 2017. "Robust estimators under a functional common principal components model," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 424-440.
    17. Gina-Maria Pomann & Ana-Maria Staicu & Sujit Ghosh, 2016. "A two-sample distribution-free test for functional data with application to a diffusion tensor imaging study of multiple sclerosis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(3), pages 395-414, April.
    18. Holger Dette & Kevin Kokot & Stanislav Volgushev, 2020. "Testing relevant hypotheses in functional time series via self‐normalization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 629-660, July.

    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:99:y:2012:i:4:p:813-832. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.