Title: Exploratory tools for outlier detection in compositional data with structural zeros
Authors : Templ, Matthias
Hron, K.
Filzmoser, P.
Published in : Journal of Applied Statistics
Volume(Issue) : 44
Issue : 4
Pages : 734
Pages to: 752
Publisher / Ed. Institution : Taylor & Francis
Issue Date: 2016
License (according to publishing contract) : Licence according to publishing contract
Type of review: Peer review (Publication)
Language : English
Subject (DDC) : 500: Natural sciences and mathematics
Abstract: The analysis of compositional data using the log-ratio approach is based on ratios between the compositional parts. Zeros in the parts thus cause serious difficulties for the analysis. This is a particular problem in case of structural zeros, which cannot be simply replaced by a non-zero value as it is done, e.g. for values below detection limit or missing values. Instead, zeros to be incorporated into further statistical processing. The focus is on exploratory tools for identifying outliers in compositional data sets with structural zeros. For this purpose, Mahalanobis distances are estimated, computed either directly for subcompositions determined by their zero patterns, or by using imputation to improve the efficiency of the estimates, and then proceed to the subcompositional and subgroup level. For this approach, new theory is formulated that allows to estimate covariances for imputed compositional data and to apply estimations on subgroups using parts of this covariance matrix. Moreover, the zero pattern structure is analyzed using principal component analysis for binary data to achieve a comprehensive view of the overall multivariate data structure. The proposed tools are applied to larger compositional data sets from official statistics, where the need for an appropriate treatment of zeros is obvious.
Departement: School of Engineering
Organisational Unit: Institute of Data Analysis and Process Design (IDP)
Publication type: Article in scientific Journal
DOI : 10.1080/02664763.2016.1182135
ISSN: 0266-4763
URI: https://digitalcollection.zhaw.ch/handle/11475/5693
Appears in Collections:Publikationen School of Engineering

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