Article
Full entry |
PDF
(0.5 MB)
Feedback
PDF
(0.5 MB)
Feedback
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
Summary:
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.
References:
[1] Aitchison J.: The statistical analysis of compositional data. : Chapman and Hall, London. 1986. MR 0865647
[2] Aitchison J., Greenacre M.: Biplots of compositional data. Applied Statistics 51 (2002), 375–392. MR 1977249 | Zbl 1111.62300
[3] Billheimer D.: Compositional data in biomedical research. In: Mateu-Figueras, G., Barceló-Vidal, C.: Compositional Data Analysis Workshop – CoDaWork’05, Proceedings, Universitat de Girona, 2005.
[4] Buccianti A., Pawlowsky-Glahn V.: New perspectives on water chemistry and compositional data analysis. Math. Geol. 37 (2005), 703–727. Zbl 1103.62111
[5] Buccianti A., Mateu-Figueras G., Pawlowsky-Glahn V. (eds): Compositional data analysis in the geosciences: From theory to practice. : Geological Society, London, Special Publications. 264, 2006.
[6] Egozcue J. J., Pawlowsky-Glahn V., Mateu-Figueraz G., Barceló-Vidal C.: Isometric logratio transformations for compositional data analysis. Math. Geol. 35 (2003), 279–300. MR 1986165
[7] Egozcue J. J., Pawlowsky-Glahn V.: Groups of parts and their balances in compositional data analysis. Math. Geol. 37 (2005), 795–828. MR 2183639 | Zbl 1177.86018
[8] Egozcue J. J., Pawlowsky-Glahn V.: Simplicial geometry for compositional data. In: Buccianti, A., Mateu-Figueras, G., Pawlowsky-Glahn, V. (eds.): Compositional data analysis in the geosciences: From theory to practice. Geological Society, London, Special Publications 264 (2006), 145–160. Zbl 1156.86307
[9] Filzmoser P., Hron K.: Outlier detection for compositional data using robust methods. Math. Geosci. 40 (2008), 233–248. Zbl 1135.62040
[10] Mateu-Figueras G., Pawlowsky-Glahn V., Barceló-Vidal C.: Distributions on the simplex. In: Thió-Henestrosa, S., Martín-Fernández, J.A.: Compositional Data Analysis Workshop – CoDaWork’03, Proceedings, Universitat de Girona, 2003.
[11] Pawlowsky-Glahn V., Egozcue J. J.: Geometric approach to statistical analysis on the simplex. Stoch. Envir. Res. and Risk Ass. 15 (2001), 384–398. Zbl 0987.62001
[13] Talašová J.: Fuzzy methods for multicriteria evaluation, decision making. : Publishing House of Palacký University, Olomouc. 2006 (in Czech).
[14] Weltje G. J.: Ternary sandstone composition and provenance: an evaluation of the ‘Dickinson model’. In: Buccianti, A., Mateu-Figueras, G., Pawlowsky-Glahn, V. (eds.): Compositional data analysis in the geosciences: From theory to practice. Geological Society, London, Special Publications 264 (2006), 79–99.
Search
Partner of
