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Structural components in functional data.

Park, Juhyun and Gasser, Theo and Rousson, Valentin (2009) Structural components in functional data. Computational Statistics and Data Analysis, 53 (9). pp. 3452-3465. ISSN 0167-9473

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    Abstract

    Analyzing functional data often leads to finding common factors, for which functional principal component analysis proves to be a useful tool to summarize and characterize the random variation in a function space. The representation in terms of eigenfunctions is optimal in the sense of L2 approximation. However, the eigenfunctions are not always directed towards an interesting and interpretable direction in the context of functional data and thus could obscure the underlying structure. To overcome such difficulty, an alternative to functional principal component analysis is proposed that produces directed components which may be more informative and easier to interpret. These structural components are similar to principal components, but are adapted to situations in which the domain of the function may be decomposed into disjoint intervals such that there is effectively independence between intervals and positive correlation within intervals. The approach is demonstrated with synthetic examples as well as real data. Properties for special cases are also studied.

    Item Type: Article
    Journal or Publication Title: Computational Statistics and Data Analysis
    Additional Information: The final, definitive version of this article has been published in the Journal, Computational Statistics & Data Analysis 53 (9), 2009, © ELSEVIER.
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 20799
    Deposited By: Dr Juhyun Park
    Deposited On: 02 Dec 2008 09:41
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Apr 2014 20:24
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/20799

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