Outlier Detection for Compositional Data Using Robust Methods

摘要

Outlier detection based on the Mahalanobis distance (MD) requires an ap-propriate 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 dimen-sion the MDs of closed and opened data give an impression of the multivariate data behavior.