IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v119y2024i546p1473-1485.html
   My bibliography  Save this article

Adaptive Functional Thresholding for Sparse Covariance Function Estimation in High Dimensions

Author

Listed:
  • Qin Fang
  • Shaojun Guo
  • Xinghao Qiao

Abstract

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this article, we consider estimating sparse covariance functions for high-dimensional functional data, where the number of random functions p is comparable to, or even larger than the sample size n. Aided by the Hilbert–Schmidt norm of functions, we introduce a new class of functional thresholding operators that combine functional versions of thresholding and shrinkage, and propose the adaptive functional thresholding estimator by incorporating the variance effects of individual entries of the sample covariance function into functional thresholding. To handle the practical scenario where curves are partially observed with errors, we also develop a nonparametric smoothing approach to obtain the smoothed adaptive functional thresholding estimator and its binned implementation to accelerate the computation. We investigate the theoretical properties of our proposals when p grows exponentially with n under both fully and partially observed functional scenarios. Finally, we demonstrate that the proposed adaptive functional thresholding estimators significantly outperform the competitors through extensive simulations and the functional connectivity analysis of two neuroimaging datasets. Supplementary materials for this article are available online.

Suggested Citation

  • Qin Fang & Shaojun Guo & Xinghao Qiao, 2024. "Adaptive Functional Thresholding for Sparse Covariance Function Estimation in High Dimensions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(546), pages 1473-1485, April.
  • Handle: RePEc:taf:jnlasa:v:119:y:2024:i:546:p:1473-1485
    DOI: 10.1080/01621459.2023.2200522
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2023.2200522
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/01621459.2023.2200522?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 search for a different version of it.

    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:taf:jnlasa:v:119:y:2024:i:546:p:1473-1485. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    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.