Remark on properties of bases for additive logratio transformations of compositional data
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2008)
- Volume: 47, Issue: 1, page 77-82
- ISSN: 0231-9721
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topHron, Karel. "Remark on properties of bases for additive logratio transformations of compositional data." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 47.1 (2008): 77-82. <http://eudml.org/doc/32465>.
@article{Hron2008,
abstract = {The statistical analysis of compositional data, multivariate data when all its components are strictly positive real numbers that carry only relative information and having a simplex as the sample space, is in the state-of-the-art devoted to represent compositions in orthonormal bases with respect to the geometry on the simplex and thus provide an isometric transformation of the data to an usual linear space, where standard statistical methods can be used (e.g. [2], [4], [5], [9]). However, in some applications from geosciences ([14]) or statistical aspects of multicriteria evaluation theory ([13]) it seems to be convenient to use another types of bases. This paper is devoted to describe its basic properties and illustrate the results on an example.},
author = {Hron, Karel},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Aitchison geometry on the simplex; bases on the simplex; additive logratio transformations; Aitchison geometry on the simplex; bases on the simplex; additive logratio transformations},
language = {eng},
number = {1},
pages = {77-82},
publisher = {Palacký University Olomouc},
title = {Remark on properties of bases for additive logratio transformations of compositional data},
url = {http://eudml.org/doc/32465},
volume = {47},
year = {2008},
}
TY - JOUR
AU - Hron, Karel
TI - Remark on properties of bases for additive logratio transformations of compositional data
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2008
PB - Palacký University Olomouc
VL - 47
IS - 1
SP - 77
EP - 82
AB - The statistical analysis of compositional data, multivariate data when all its components are strictly positive real numbers that carry only relative information and having a simplex as the sample space, is in the state-of-the-art devoted to represent compositions in orthonormal bases with respect to the geometry on the simplex and thus provide an isometric transformation of the data to an usual linear space, where standard statistical methods can be used (e.g. [2], [4], [5], [9]). However, in some applications from geosciences ([14]) or statistical aspects of multicriteria evaluation theory ([13]) it seems to be convenient to use another types of bases. This paper is devoted to describe its basic properties and illustrate the results on an example.
LA - eng
KW - Aitchison geometry on the simplex; bases on the simplex; additive logratio transformations; Aitchison geometry on the simplex; bases on the simplex; additive logratio transformations
UR - http://eudml.org/doc/32465
ER -
References
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