PROPAGATION OF OUTLIERS IN MULTIVARIATE DATA

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PROPAGATION OF OUTLIERS IN MULTIVARIATE DATA

TitlePROPAGATION OF OUTLIERS IN MULTIVARIATE DATA
Publication TypeJournal Article
Year of Publication2009
AuthorsAlqallaf, F, Van Aelst, S, Yohai, VJ, Zamar, RH
JournalANNALS OF STATISTICS
Volume37
Pagination311-331
Date PublishedFEB
Type of ArticleArticle
ISSN0090-5364
Keywordsbreakdown point, contamination model, independent contamination, influence function, Robustness
AbstractWe investigate the performance of robust estimates of multivariate location under nonstandard data contamination models such as componentwise outliers (i.e., contamination in each variable is independent from the other variables). This model brings up a possible new source of statistical error that we call ``propagation of outliers.'' This source of error is Unusual in the sense that it is generated by the data processing itself and takes place after the data has been collected. We define and derive the influence function of robust multivariate location estimates under flexible contamination models and use it to investigate the effect of propagation of outliers. Furthermore, we show that standard high-breakdown affine equivariant estimators propagate outliers and therefore show poor breakdown behavior under componentwise contamination when the dimension d is high.
DOI10.1214/07-AOS588