Open Access
February 2009 Propagation of outliers in multivariate data
Fatemah Alqallaf, Stefan Van Aelst, Victor J. Yohai, Ruben H. Zamar
Ann. Statist. 37(1): 311-331 (February 2009). DOI: 10.1214/07-AOS588


We 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.


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Fatemah Alqallaf. Stefan Van Aelst. Victor J. Yohai. Ruben H. Zamar. "Propagation of outliers in multivariate data." Ann. Statist. 37 (1) 311 - 331, February 2009.


Published: February 2009
First available in Project Euclid: 16 January 2009

zbMATH: 1155.62043
MathSciNet: MR2488353
Digital Object Identifier: 10.1214/07-AOS588

Primary: 62F35
Secondary: 62H12

Keywords: Breakdown point , contamination model , independent contamination , influence function , robustness

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 1 • February 2009
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