IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v68y1999i1p120-137.html
   My bibliography  Save this article

Rates of Convergence for Spline Estimates of Additive Principal Components

Author

Listed:
  • El Faouzi, Nour Eddin
  • Sarda, Pascal

Abstract

Additive principal components(APCs) generalize classicalprincipal component analysisto additive nonlinear transformations.Smallest APCsare additive functions of the vectorX=(X1, ..., Xp) minimizing the variance under orthogonality constraints and are characterized as eigenfunctions of an operator which is compact under a standard condition on the joint distribution of (X1, ..., Xp). As a by-product,smallest APCnearly satisfies the equation [summation operator]j [phi]j(Xj)=0 and then provides powerful tools for regression and data analysis diagnostics. The principal aim of this paper is the estimation of smallest APCs based on a sample from the distribution ofX. This is achieved using additive splines, which have been recently investigated in several functional estimation problems. The rates of convergence are then derived under mild conditions on the component functions. These rates are the same as the optimal rates for a nonparametric estimate of a univariate regression function.

Suggested Citation

  • El Faouzi, Nour Eddin & Sarda, Pascal, 1999. "Rates of Convergence for Spline Estimates of Additive Principal Components," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 120-137, January.
  • Handle: RePEc:eee:jmvana:v:68:y:1999:i:1:p:120-137
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(98)91781-X
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Salinelli, Ernesto, 2009. "Nonlinear principal components, II: Characterization of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 652-660, April.

    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:eee:jmvana:v:68:y:1999:i:1:p:120-137. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.