Nonparametric geometric outlier detection

Matias Heikkilä*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


Outlier detection is a major topic in robust statistics due to the high practical significance of anomalous observations. Many existing methods, however, either are parametric or cease to perform well when the data are far from linearly structured. In this paper, we propose a quantity, Delaunay outlyingness, that is a nonparametric outlyingness score applicable to data with complicated structure. The approach is based on a well-known triangulation of the sample, which seems to reflect the sparsity of the pointset to different directions in a useful way. We derive results on the asymptotic behavior of Delaunay outlyingness in case of a sufficiently simple set of observations. Simulations and an application to empirical data are also discussed.

Original languageEnglish
Pages (from-to)1300-1314
Number of pages15
JournalScandinavian Journal of Statistics
Issue number4
Early online date1 Jan 2019
Publication statusPublished - Dec 2019
MoE publication typeA1 Journal article-refereed


  • Delaunay triangulation
  • robust statistics
  • Voronoi diagram


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