Outlier Detection for Compositional Data Using Robust Methods |
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Authors: | Peter Filzmoser Karel Hron |
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Institution: | (1) Dept. of Statistics and Probability Theory, Vienna University of Technology, Wiedner Hauptstr. 8-10, 1040 Vienna, Austria;(2) Dept. of Mathematical Analysis and Applications of Mathematics, Palacky University Olomouc, Tomkova 40, 77100 Olomouc, Czech Republic |
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Abstract: | 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. |
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Keywords: | Mahalanobis distance Robust statistics Ternary diagram Multivariate outliers Logratio transformation |
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