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    Functional Boxplots

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    Type
    Article
    Authors
    Sun, Ying cc
    Genton, Marc G. cc
    KAUST Grant Number
    KUS-C1-016-04
    Date
    2011-01
    Permanent link to this record
    http://hdl.handle.net/10754/598381
    
    Metadata
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    Abstract
    This article proposes an informative exploratory tool, the functional boxplot, for visualizing functional data, as well as its generalization, the enhanced functional boxplot. Based on the center outward ordering induced by band depth for functional data, the descriptive statistics of a functional boxplot are: the envelope of the 50% central region, the median curve, and the maximum non-outlying envelope. In addition, outliers can be detected in a functional boxplot by the 1.5 times the 50% central region empirical rule, analogous to the rule for classical boxplots. The construction of a functional boxplot is illustrated on a series of sea surface temperatures related to the El Niño phenomenon and its outlier detection performance is explored by simulations. As applications, the functional boxplot and enhanced functional boxplot are demonstrated on children growth data and spatio-temporal U.S. precipitation data for nine climatic regions, respectively. This article has supplementary material online. © 2011 American Statistical Association.
    Citation
    Sun Y, Genton MG (2011) Functional Boxplots. Journal of Computational and Graphical Statistics 20: 316–334. Available: http://dx.doi.org/10.1198/jcgs.2011.09224.
    Sponsors
    This research was partially supported by NSF grants CMG ATM-0620624, DMS-1007504, and award no. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The authors thank the editor, an associate editor, and three anonymous referees for their valuable comments.
    Publisher
    Informa UK Limited
    Journal
    Journal of Computational and Graphical Statistics
    DOI
    10.1198/jcgs.2011.09224
    ae974a485f413a2113503eed53cd6c53
    10.1198/jcgs.2011.09224
    Scopus Count
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