2009/01/16 by Fatemah Alqallaf, Stefan Van Aelst, Victor J. Yohai +2 · 6 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #Probabilistic and Robust Engineering Design #math.ST #msc:62F35 #msc:62H12 #stat.TH
paper · pdf · doi:10.1214/07-aos588
published as Annals of Statistics 2009, Vol. 37, No. 1, 311-331 · Published in at http://dx.doi.org/10.1214/07-AOS588 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2009/01/16 · arxiv created 2009/03/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.