Journal
COMPUTATIONAL STATISTICS
Volume 27, Issue 4, Pages 585-604Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00180-011-0279-8
Keywords
Compositional data; Logratio transformations; Discriminant analysis; Robustness
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Funding
- Council of the Czech Government [MSM 6198959214]
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Compositional data, i.e. data including only relative information, need to be transformed prior to applying the standard discriminant analysis methods that are designed for the Euclidean space. Here it is investigated for linear, quadratic, and Fisher discriminant analysis, which of the transformations lead to invariance of the resulting discriminant rules. Moreover, it is shown that for robust parameter estimation not only an appropriate transformation, but also affine equivariant estimators of location and covariance are needed. An example and simulated data demonstrate the effects of working in an inappropriate space for discriminant analysis.
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