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The mathematics of compositional analysis

The term compositional data analysis is historically associated to the approach based on the logratio transformations introduced in the eighties. Two main principles of this methodology are scale invariance and subcompositional coherence. New developments and concepts emerged in the last decade revealed the need to clarify the concepts of compositions, compositional sample space and subcomposition. In this work the mathematics of compositional analysis based on equivalence relation is presented. A logarithmic isomorphism between quotient spaces induces a metric space structure for compositions. The logratio compositional analysis is the statistical analysis of compositions based on this structure, consisting of analysing logratio coordinates

This work has been partially nanced by the Ministerio de Econom a y Competitividad (Ref: MTM2015-65016-C2-1-R) and the Ag encia de Gesti o d’Ajuts Universitaris i de Re- cerca (AGAUR), Generalitat de Catalunya (Ref: 2014 SGR 551)

Austrian Society for Statistics

Manager: Ministerio de Economía y Competitividad (Espanya)
Generalitat de Catalunya. Agència de Gestió d’Ajuts Universitaris i de Recerca
Author: Barceló i Vidal, Carles
Martín Fernández, Josep Antoni
Date: 2016 January 1
Abstract: The term compositional data analysis is historically associated to the approach based on the logratio transformations introduced in the eighties. Two main principles of this methodology are scale invariance and subcompositional coherence. New developments and concepts emerged in the last decade revealed the need to clarify the concepts of compositions, compositional sample space and subcomposition. In this work the mathematics of compositional analysis based on equivalence relation is presented. A logarithmic isomorphism between quotient spaces induces a metric space structure for compositions. The logratio compositional analysis is the statistical analysis of compositions based on this structure, consisting of analysing logratio coordinates
This work has been partially nanced by the Ministerio de Econom a y Competitividad (Ref: MTM2015-65016-C2-1-R) and the Ag encia de Gesti o d’Ajuts Universitaris i de Re- cerca (AGAUR), Generalitat de Catalunya (Ref: 2014 SGR 551)
Format: application/pdf
Document access: http://hdl.handle.net/10256/13052
Language: eng
Publisher: Austrian Society for Statistics
Collection: info:eu-repo/semantics/altIdentifier/doi/10.17713/ajs.v45i4.142
info:eu-repo/semantics/altIdentifier/issn/1026-597X
info:eu-repo/grantAgreement/MINECO//MTM2015-65016-C2-1-R/ES/ANALISIS DE DATOS COMPOSICIONALES Y METODOS RELACIONADOS/
AGAUR/2014-2016/2014 SGR-551
Rights: Attribution 3.0 Spain
Rights URI: http://creativecommons.org/licenses/by/3.0/es/
Subject: Anàlisi multivariable
Multivariate analysis
Estadística matemàtica
Mathematical statistics
Title: The mathematics of compositional analysis
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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