Classical and robust orthogonal regression between parts of compositional data

The different parts (variables) of a compositional data set cannot be considered independent from each other, since only the ratios between the parts constitute the relevant information to be analysed. Practically, this information can be included in a system of orthonormal coordinates. For the task...

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Published inStatistics (Berlin, DDR) Vol. 50; no. 6; pp. 1261 - 1275
Main Authors Hrůzová, K., Todorov, V., Hron, K., Filzmoser, P.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.11.2016
Taylor & Francis Ltd
Subjects
bootstrap inference
Compositional data
Economic analysis
isometric log-ratio coordinates
MM-estimates
orthogonal regression
Parameter estimation
Parameter robustness
Principal components analysis
Regression analysis
Robustness (mathematics)
Statistical analysis
Statistical inference
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Abstract The different parts (variables) of a compositional data set cannot be considered independent from each other, since only the ratios between the parts constitute the relevant information to be analysed. Practically, this information can be included in a system of orthonormal coordinates. For the task of regression of one part on other parts, a specific choice of orthonormal coordinates is proposed which allows for an interpretation of the regression parameters in terms of the original parts. In this context, orthogonal regression is appropriate since all compositional parts - also the explanatory variables - are measured with errors. Besides classical (least-squares based) parameter estimation, also robust estimation based on robust principal component analysis is employed. Statistical inference for the regression parameters is obtained by bootstrap; in the robust version the fast and robust bootstrap procedure is used. The methodology is illustrated with a data set from macroeconomics.
AbstractList The different parts (variables) of a compositional data set cannot be considered independent from each other, since only the ratios between the parts constitute the relevant information to be analysed. Practically, this information can be included in a system of orthonormal coordinates. For the task of regression of one part on other parts, a specific choice of orthonormal coordinates is proposed which allows for an interpretation of the regression parameters in terms of the original parts. In this context, orthogonal regression is appropriate since all compositional parts - also the explanatory variables - are measured with errors. Besides classical (least-squares based) parameter estimation, also robust estimation based on robust principal component analysis is employed. Statistical inference for the regression parameters is obtained by bootstrap; in the robust version the fast and robust bootstrap procedure is used. The methodology is illustrated with a data set from macroeconomics.
Author Hrůzová, K.
Todorov, V.
Filzmoser, P.
Hron, K.
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Snippet The different parts (variables) of a compositional data set cannot be considered independent from each other, since only the ratios between the parts...
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SubjectTerms bootstrap inference
Compositional data
Economic analysis
isometric log-ratio coordinates
MM-estimates
orthogonal regression
Parameter estimation
Parameter robustness
Principal components analysis
Regression analysis
Robustness (mathematics)
Statistical analysis
Statistical inference
Title Classical and robust orthogonal regression between parts of compositional data
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Volume 50
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