Propagation of outliers in multivariate data

Details Propagation of outliers in multivariate data Propagation of outliers in multivariate data

2009-03-03

arxiv.org/abs/0903.0447v1

Annals of Statistics 2009, Vol. 37, No. 1, 311-331

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS588 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

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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