Rainbow plots, bagplots, and boxplots for functional data

Rob J. Hyndman, Han Lin Shang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

173 Citations (Scopus)


We propose new tools for visualizing large amounts of functional data in the form of smooth curves. The proposed tools include functional versions of the bagplot and boxplot, which make use of the first two robust principal component scores, Tukey’s data depth and highest density regions.

By-products of our graphical displays are outlier detection methods for functional data. We compare these new outlier detection methods with existing methods for detecting outliers in functional data, and show that our methods are better able to identify outliers.

An R-package containing computer code and datasets is available in the online supplements.
Original languageEnglish
Pages (from-to)29-45
Number of pages17
JournalJournal of Computational and Graphical Statistics
Issue number1
Publication statusPublished - 2010
Externally publishedYes


  • Highest density regions
  • Kernel density estimation
  • Outlier detection
  • Robust principal component analysis
  • Tukey’s halfspace location depth


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