Functional Boxplots

Ying Sun*, Marc G. Genton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

307 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)316-334
Number of pages19
JournalJournal of Computational and Graphical Statistics
Issue number2
StatePublished - Jan 2011
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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