Extremal Depth for Functional Data and Applications

Naveen N. Narisetty, Vijayan N. Nair

Research output: Contribution to journalArticlepeer-review


We propose a new notion called “extremal depth” (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme “outlyingness.” ED has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces. In particular: (a) the central region achieves the nominal (desired) simultaneous coverage probability; (b) there is a correspondence between ED-based (simultaneous) central regions and appropriate pointwise central regions; and (c) the method is resistant to certain classes of functional outliers. The article examines the performance of ED and compares it with other depth notions. Its usefulness is demonstrated through applications to constructing central regions, functional boxplots, outlier detection, and simultaneous confidence bands in regression problems. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1705-1714
Number of pages10
JournalJournal of the American Statistical Association
Issue number516
StatePublished - Oct 1 2016
Externally publishedYes


  • Central regions
  • Data depth
  • Functional boxplots
  • Outlier detection
  • Simultaneous inference

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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