Robust coordinates for compositional data using weighted balances

Kód výsledku v 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>

Výsledek na webu

—

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

Robust coordinates for compositional data using weighted balances

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Robust coordinates for compositional data using weighted balances

Popis výsledku anglicky

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.

Druh

C - Kapitola v odborné knize

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/EE2.3.20.0170" target="_blank" >EE2.3.20.0170: Budování výzkumně-vzdělávacího týmu v oblasti modelování přírodních jevů a využití geoinformačních systémů, s vazbou na zapojení do mezinárodních sítí a programů.</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Modern nonparametric, robust and multivariate methods

ISBN

978-3-319-22403-9

Počet stran výsledku

18

Strana od-do

167-184

Počet stran knihy

506

Název nakladatele

Springer International Publishing

Místo vydání

Heidelberg

Kód UT WoS kapitoly

—