The Annals of Statistics

Propagation of outliers in multivariate data

Fatemah Alqallaf, Stefan Van Aelst, Victor J. Yohai, and Ruben H. Zamar

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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.

Article information

Ann. Statist., Volume 37, Number 1 (2009), 311-331.

First available in Project Euclid: 16 January 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F35: Robustness and adaptive procedures
Secondary: 62H12: Estimation

Breakdown point contamination model independent contamination influence function robustness


Alqallaf, Fatemah; Van Aelst, Stefan; Yohai, Victor J.; Zamar, Ruben H. Propagation of outliers in multivariate data. Ann. Statist. 37 (2009), no. 1, 311--331. doi:10.1214/07-AOS588.

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