Robust coordinates for compositional data using weighted balances

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F15%3A33159867" target="_blank" >RIV/61989592:15310/15:33159867 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Robust coordinates for compositional data using weighted balances
Original language description
Multivariate observations which carry exclusively relative information are known under the name compositional data, and they have very specific geometrical properties. In order to represent them in the usual Euclidean geometry, they need to be expressed in orthonormal coordinates prior to their possible further statistical processing. As it is not possible to construct Cartesian coordinates for the compositions, that would assign a coordinate for each of the parts separately, a choice of interpretable orthonormal coordinates is of particular interest. Although recent experiences show clear advantages of such coordinates, where the first coordinate aggregates information from logratios with a particular compositional part of interest, their usefulness is limited if there are distortions like rounding errors or other data problems in the involved parts. The aim of the paper is thus to introduce a "robust" version of these coordinates, where the role of the remaining parts (with respect to the part of interest) is weighted according to their relevance for the purpose of the statistical analysis. Theoretical considerations are accompanied by examples with data sets from chemistry and geochemistry, pointing out the role of robust estimation in the context of regression with compositional covariates.
Czech name
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Czech description
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Project
<a href="/en/project/EE2.3.20.0170" target="_blank" >EE2.3.20.0170: Building of Research Team in the Field of Environmental Modeling and the Use of Geoinformation Systems with the Consequence in Participation in International Networks and Programs</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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