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    Simplicial band depth for multivariate functional data

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    Type
    Article
    Authors
    López-Pintado, Sara
    Sun, Ying cc
    Lin, Juan K.
    Genton, Marc G. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Spatio-Temporal Statistics and Data Analysis Group
    Date
    2014-03-05
    Online Publication Date
    2014-03-05
    Print Publication Date
    2014-09
    Permanent link to this record
    http://hdl.handle.net/10754/563434
    
    Metadata
    Show full item record
    Abstract
    We propose notions of simplicial band depth for multivariate functional data that extend the univariate functional band depth. The proposed simplicial band depths provide simple and natural criteria to measure the centrality of a trajectory within a sample of curves. Based on these depths, a sample of multivariate curves can be ordered from the center outward and order statistics can be defined. Properties of the proposed depths, such as invariance and consistency, can be established. A simulation study shows the robustness of this new definition of depth and the advantages of using a multivariate depth versus the marginal depths for detecting outliers. Real data examples from growth curves and signature data are used to illustrate the performance and usefulness of the proposed depths. © 2014 Springer-Verlag Berlin Heidelberg.
    Citation
    López-Pintado, S., Sun, Y., Lin, J. K., & Genton, M. G. (2014). Simplicial band depth for multivariate functional data. Advances in Data Analysis and Classification, 8(3), 321–338. doi:10.1007/s11634-014-0166-6
    Publisher
    Springer Nature
    Journal
    Advances in Data Analysis and Classification
    DOI
    10.1007/s11634-014-0166-6
    ae974a485f413a2113503eed53cd6c53
    10.1007/s11634-014-0166-6
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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