Outlier Detection for Compositional Data Using Robust Methods
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Outlier detection based on the Mahalanobis distance (MD) requires an appropriate transformation in case of compositional data. For the family of logratio transformations (additive, centered and isometric logratio transformation) it is shown that the MDs based on classical estimates are invariant to these transformations, and that the MDs based on affine equivariant estimators of location and covariance are the same for additive and isometric logratio transformation. Moreover, for 3-dimensional compositions the data structure can be visualized by contour lines. In higher dimension the MDs of closed and opened data give an impression of the multivariate data behavior.
KeywordsMahalanobis distance Robust statistics Ternary diagram Multivariate outliers Logratio transformation
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- Aitchison J (1986) The statistical analysis of compositional data. Monographs on statistics and applied probability. Chapman & Hall, London, 416 p Google Scholar
- Coakley JP, Rust BR (1968) Sedimentation in an Arctic lake. J Sed Pet 38(4):1290–1300. Quoted in Aitchison (1986), the statistical analysis of compositional data. Chapman & Hall, London, 416 p Google Scholar
- Harville DA (1997) Matrix algebra from a statistician’s perspective. Springer, New York, 630 p Google Scholar
- R development core team, 2006, R: A language and environment for statistical computing. Vienna. http://www.r-project.org
- Reimann C, Äyräs M, Chekushin V, Bogatyrev I, Boyd R, Caritat P. d., Dutter R, Finne T, Halleraker J, Jæger O, Kashulina G, Lehto O, Niskavaara H, Pavlov V, Räisänen M, Strand T, Volden T (1998) Environmental geochemical atlas of the Central Barents Region: Geological Survey of Norway (NGU), Geological Survey of Finland (GTK), and Central Kola Expedition (CKE), Special Publication, Trondheim, Espoo, Monchegorsk, 745 p Google Scholar
- Rousseeuw PJ, Leroy AM (2003) Robust regression and outlier detection. Wiley, New York, 360 p Google Scholar
- Thompson RN, Esson J, Duncan AC (1972) Major element chemical variation in the Eocene lavas of the Isle of Skye Scotland. J Petrol 13(2):219–253. Quoted in Aitchison, J., 1986, The statistical analysis of compositional data. Chapman & Hall, London, 416 p Google Scholar