COMPUTATIONAL STATISTICS & DATA ANALYSIS vol:56 issue:3 pages:531-542
The Stahel-Donoho estimator is dened as a weighted mean and covariance,
where the weight of each observation depends on a measure of its outlyingness.
In high dimensions, it can easily happen that an amount of outlying measure-
ments is present in such a way that the majority of the observations is contami-
nated in at least one of its components. In these situations, the Stahel-Donoho
estimator has diculties in identifying the actual outlyingness of the contami-
nated observations. An adaptation of the Stahel-Donoho estimator is presented
where the data are huberized before the outlyingness is computed. It is shown
that the huberized outlyingness better re ects the actual outlyingness of each
observation towards the non-contaminated observations. Therefore, the result-
ing adapted Stahel-Donoho estimator can better withstand large amounts of
outliers. It is demonstrated that the Stahel-Donoho estimator based on huber-
ized outlyingness works especially well when the data are heavily contaminated.