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oai:recercat.cat:10256/130522024-06-18T12:16:40Zcom_2072_452955com_2072_2054col_2072_453069

The mathematics of compositional analysis Barceló i Vidal, Carles Martín Fernández, Josep Antoni Anàlisi multivariable Multivariate analysis Estadística matemàtica Mathematical statistics 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) 2024-06-18T12:16:40Z 2024-06-18T12:16:40Z 2024-06-18T12:16:40Z 2016-01-01 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://hdl.handle.net/10256/13052 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 Attribution 3.0 Spain http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Austrian Society for Statistics © Austrian Journal of Statistics, 2016, vol. 45, núm. 4, p. 57-71 Articles publicats (D-IMA)