Title

An affine equivariant anamorphosis for compositional data [Conference paper]

Document Type

Conference Proceeding

Publication Title

Proceedings of IAMG 2015 - 17th Annual Conference of the International Association for Mathematical Geosciences

Publisher

International Association for Mathematical Geosciences

School

School of Science

RAS ID

21623

Comments

Originally published as: van den Boogaart, K. G., Tolosana-Delgado, R., & Mueller, U. (2015). An affine equivariant anamorphosis for compositional data. In Proceedings of IAMG 2015 - 17th Annual Conference of the International Association for Mathematical Geosciences (pp. 1302-1311). Freiberg, Germany: International Association for Mathematical Geosciences. Original publication available here

Abstract

For the geostatistical treatment of compositional data it is common to transform the data to logratios. Several logratio transformations are available and invariance of the results under the choice of logratio transform is desirable, but this is not automatically satisfied for geostatistical simulation where it is common that the data are first mapped to Gaussian space. The usual method, the normal score transform, is not independent of the choice of logratio nor are the transformed data multivariate normal. In this contribution a method is proposed based on an affine-equivariant kernel density estimation, which is then continuously deformed to a multivariate standard normal distribution. The anamorphosis is achieved via the co-deformation of the underlying space. The method is illustrated and compared with existing alternatives using a case study from a West Australian iron ore mining operation.

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