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Mathematical Geosciences

, Volume 49, Issue 2, pp 231–251 | Cite as

An Affine Equivariant Multivariate Normal Score Transform for Compositional Data

  • K. Gerald van den Boogaart
  • Ute Mueller
  • Raimon Tolosana-Delgado
Article

Abstract

The geostatistical treatment of continuous variables often includes a transformation to normal scores. In the case of analysing a composition, it has been suggested that standard methods can be applied to (isometric) logratio transformed compositions. Several logratio transformations are available and invariance of the final results under the choice of logratio transform is desirable. However, a geostatistical procedure which includes marginal normal scores transformations of the individual logratio scores via quantile matching will not have this invariance property, nor will the resulting vectors of scores show a joint multivariate normal distribution. In this paper an affine-equivariant normal score transform is proposed. The method is based on a continuous deformation of the underlying logratio space to a Gaussian space. The properties and performance of this method are illustrated and compared with existing alternatives using a simulated setting and a case study from a banded iron formation ore mining operation from Western Australia. The proposed method is also suitable for the study of other multivariate non-compositional cases.

Keywords

Additive logratio transform Flow Gaussian anamorphosis Ordinary differential equation 

Notes

Acknowledgments

The authors acknowledge financial support through the ECU CES Travel Scheme 2014 and the DAAD-UA Grant CodaBlockKriging.

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Copyright information

© International Association for Mathematical Geosciences 2016

Authors and Affiliations

  • K. Gerald van den Boogaart
    • 1
  • Ute Mueller
    • 2
  • Raimon Tolosana-Delgado
    • 1
  1. 1.Helmholtz Zentrum Dresden-RossendorfHelmholtz Institute Freiberg for Resource TechnologyFreibergGermany
  2. 2.School of ScienceEdith Cowan UniversityPerthAustralia

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