IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

On the definition of phase and amplitude variability in functional data analysis

  • Simone Vantini

    ()

Registered author(s):

    We introduce a modeling and mathematical framework in which the problem of registering a functional data set can be consistently set. In detail, we show that the introduction, in a functional data analysis, of a metric/semi-metric and of a group of warping functions, with respect to which the metric/semi-metric is invariant, enables a sound and not ambiguous definition of phase and amplitude variability. Indeed, in this framework, we prove that the analysis of a registered functional data set can be re-interpreted as the analysis of a set of suitable equivalence classes associated to original functions and induced by the group of the warping functions. Moreover, an amplitude-to-total variability index is proposed. This index turns out to be useful in practical situations for measuring to what extent phase variability affects the data and for comparing the effectiveness of different registration methods. Copyright Sociedad de Estadística e Investigación Operativa 2012

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://hdl.handle.net/10.1007/s11749-011-0268-9
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Springer in its journal TEST.

    Volume (Year): 21 (2012)
    Issue (Month): 4 (December)
    Pages: 676-696

    as
    in new window

    Handle: RePEc:spr:testjl:v:21:y:2012:i:4:p:676-696
    Contact details of provider: Web page: http://www.springerlink.com/link.asp?id=120411

    Order Information: Web: http://link.springer.de/orders.htm

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. Xueli Liu & Hans-Georg Muller, 2004. "Functional Convex Averaging and Synchronization for Time-Warped Random Curves," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 687-699, January.
    2. Kneip, Alois & Ramsay, James O, 2008. "Combining Registration and Fitting for Functional Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1155-1165.
    3. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
    4. Sangalli, Laura M. & Secchi, Piercesare & Vantini, Simone & Vitelli, Valeria, 2010. "k-mean alignment for curve clustering," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1219-1233, May.
    5. Ferraty, F., 2010. "High-dimensional data: a fascinating statistical challenge," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 305-306, February.
    6. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
    7. Mariano Valderrama, 2007. "An overview to modelling functional data," Computational Statistics, Springer, vol. 22(3), pages 331-334, September.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:21:y:2012:i:4:p:676-696. 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: (Sonal Shukla)

    or (Christopher F Baum)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.