IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v37y2010i4p577-589.html
   My bibliography  Save this article

The eigenstructure of block-structured correlation matrices and its implications for principal component analysis

Author

Listed:
  • Jorge Cadima
  • Francisco Lage Calheiros
  • Isabel Preto

Abstract

Block-structured correlation matrices are correlation matrices in which the p variables are subdivided into homogeneous groups, with equal correlations for variables within each group, and equal correlations between any given pair of variables from different groups. Block-structured correlation matrices arise as approximations for certain data sets' true correlation matrices. A block structure in a correlation matrix entails a certain number of properties regarding its eigendecomposition and, therefore, a principal component analysis of the underlying data. This paper explores these properties, both from an algebraic and a geometric perspective, and discusses their robustness. Suggestions are also made regarding the choice of variables to be subjected to a principal component analysis, when in the presence of (approximately) block-structured variables.

Suggested Citation

  • Jorge Cadima & Francisco Lage Calheiros & Isabel Preto, 2010. "The eigenstructure of block-structured correlation matrices and its implications for principal component analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(4), pages 577-589.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:4:p:577-589
    DOI: 10.1080/02664760902803263
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760902803263
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760902803263?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.

    Citations

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


    Cited by:

    1. Ilya Archakov & Peter Reinhard Hansen, 2024. "A Canonical Representation of Block Matrices with Applications to Covariance and Correlation Matrices," The Review of Economics and Statistics, MIT Press, vol. 106(4), pages 1099-1113, July.
    2. Boyle, Phelim & Jiang, Ruihong, 2023. "A note on portfolios of averages of lognormal variables," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 97-109.
    3. Gong, Tingnan & Zhang, Weiping & Chen, Yu, 2023. "Uncovering block structures in large rectangular matrices," Journal of Multivariate Analysis, Elsevier, vol. 198(C).

    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:japsta:v:37:y:2010:i:4:p:577-589. 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/CJAS20 .

    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.